LMFDB - Embedded newform 22.5.d.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,5,Mod(7,22)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("22.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	22.d (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.27413918784$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 138 x^{14} - 428 x^{13} + 7783 x^{12} - 18620 x^{11} + 235604 x^{10} + \cdots + 1499670491 $ x^16 - 4x^15 + 138x^14 - 428x^13 + 7783x^12 - 18620x^11 + 235604x^10 - 425164x^9 + 4199998x^8 - 5446172x^7 + 45313276x^6 - 38408204x^5 + 290282498x^4 - 132888724x^3 + 1016893202x^2 - 153602264*x + 1499670491
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			17.1
Root			$0.809017 - 5.77971i$ of defining polynomial
Character	$\chi$	$=$	22.17
Dual form			22.5.d.a.13.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.68999 + 0.874032i) q^{2} +(-3.20187 - 2.32629i) q^{3} +(6.47214 - 4.70228i) q^{4} +(13.3838 - 41.1910i) q^{5} +(10.6463 + 3.45918i) q^{6} +(-7.80030 - 10.7362i) q^{7} +(-13.3001 + 18.3060i) q^{8} +(-20.1901 - 62.1386i) q^{9} +O(q^{10})$	\(q+(-2.68999 + 0.874032i) q^{2} +(-3.20187 - 2.32629i) q^{3} +(6.47214 - 4.70228i) q^{4} +(13.3838 - 41.1910i) q^{5} +(10.6463 + 3.45918i) q^{6} +(-7.80030 - 10.7362i) q^{7} +(-13.3001 + 18.3060i) q^{8} +(-20.1901 - 62.1386i) q^{9} +122.501i q^{10} +(90.5882 + 80.2170i) q^{11} -31.6618 q^{12} +(-170.407 + 55.3685i) q^{13} +(30.3665 + 22.0626i) q^{14} +(-138.675 + 100.754i) q^{15} +(19.7771 - 60.8676i) q^{16} +(167.901 + 54.5543i) q^{17} +(108.622 + 149.506i) q^{18} +(213.240 - 293.500i) q^{19} +(-107.070 - 329.528i) q^{20} +52.5217i q^{21} +(-313.794 - 136.606i) q^{22} +564.946 q^{23} +(85.1701 - 27.6734i) q^{24} +(-1011.94 - 735.215i) q^{25} +(409.999 - 297.882i) q^{26} +(-178.970 + 550.813i) q^{27} +(-100.969 - 32.8069i) q^{28} +(505.658 + 695.978i) q^{29} +(284.974 - 392.233i) q^{30} +(276.141 + 849.875i) q^{31} +181.019i q^{32} +(-103.443 - 467.579i) q^{33} -499.334 q^{34} +(-546.632 + 177.611i) q^{35} +(-422.866 - 307.230i) q^{36} +(-164.418 + 119.457i) q^{37} +(-317.087 + 975.892i) q^{38} +(674.423 + 219.133i) q^{39} +(576.036 + 792.845i) q^{40} +(1540.12 - 2119.80i) q^{41} +(-45.9056 - 141.283i) q^{42} +2603.62i q^{43} +(963.502 + 93.2040i) q^{44} -2829.77 q^{45} +(-1519.70 + 493.780i) q^{46} +(-1250.87 - 908.812i) q^{47} +(-204.920 + 148.883i) q^{48} +(687.529 - 2116.00i) q^{49} +(3364.70 + 1093.26i) q^{50} +(-410.687 - 565.262i) q^{51} +(-842.537 + 1159.65i) q^{52} +(-454.551 - 1398.97i) q^{53} -1638.11i q^{54} +(4516.63 - 2657.81i) q^{55} +300.281 q^{56} +(-1365.53 + 443.689i) q^{57} +(-1968.52 - 1430.22i) q^{58} +(3977.33 - 2889.70i) q^{59} +(-423.754 + 1304.18i) q^{60} +(-1508.75 - 490.221i) q^{61} +(-1485.64 - 2044.80i) q^{62} +(-509.644 + 701.464i) q^{63} +(-158.217 - 486.941i) q^{64} +7760.26i q^{65} +(686.941 + 1167.37i) q^{66} -3004.99 q^{67} +(1343.21 - 436.434i) q^{68} +(-1808.88 - 1314.23i) q^{69} +(1315.20 - 955.547i) q^{70} +(-2625.89 + 8081.67i) q^{71} +(1406.04 + 456.849i) q^{72} +(2674.58 + 3681.24i) q^{73} +(337.875 - 465.045i) q^{74} +(1529.76 + 4708.12i) q^{75} -2902.29i q^{76} +(154.610 - 1598.29i) q^{77} -2005.72 q^{78} +(2009.88 - 653.050i) q^{79} +(-2242.51 - 1629.28i) q^{80} +(-2427.13 + 1763.41i) q^{81} +(-2290.15 + 7048.37i) q^{82} +(-8994.67 - 2922.55i) q^{83} +(246.972 + 339.927i) q^{84} +(4494.29 - 6185.86i) q^{85} +(-2275.65 - 7003.72i) q^{86} -3404.74i q^{87} +(-2673.28 + 591.414i) q^{88} +14557.2 q^{89} +(7612.06 - 2473.31i) q^{90} +(1923.67 + 1397.63i) q^{91} +(3656.40 - 2656.53i) q^{92} +(1092.89 - 3363.57i) q^{93} +(4159.17 + 1351.40i) q^{94} +(-9235.60 - 12711.7i) q^{95} +(421.104 - 579.600i) q^{96} +(2097.12 + 6454.28i) q^{97} +6292.94i q^{98} +(3155.59 - 7248.61i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9	\( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9} - 30 q^{11} - 384 q^{12} - 510 q^{13} - 96 q^{14} - 1398 q^{15} - 256 q^{16} + 1770 q^{17} + 1120 q^{18} + 1020 q^{19} - 240 q^{20} + 240 q^{22} - 2424 q^{23} - 640 q^{24} - 858 q^{25} + 480 q^{26} + 2224 q^{27} + 1600 q^{28} + 4890 q^{29} + 3360 q^{30} + 602 q^{31} - 2648 q^{33} - 3904 q^{34} - 8670 q^{35} + 720 q^{36} - 4518 q^{37} - 4800 q^{38} - 1130 q^{39} - 1280 q^{40} + 1290 q^{41} - 3808 q^{42} + 720 q^{44} + 12152 q^{45} + 4480 q^{46} + 642 q^{47} - 128 q^{48} + 9534 q^{49} + 6720 q^{50} - 1500 q^{51} + 4000 q^{52} + 2598 q^{53} + 2582 q^{55} - 3072 q^{56} + 9140 q^{57} - 6496 q^{58} + 6660 q^{59} - 5776 q^{60} - 27410 q^{61} - 19680 q^{62} - 27260 q^{63} + 2048 q^{64} + 2528 q^{66} + 21524 q^{67} + 14160 q^{68} + 11416 q^{69} + 34400 q^{70} - 5562 q^{71} + 10240 q^{72} - 7790 q^{73} + 5760 q^{74} + 3576 q^{75} - 1110 q^{77} - 39424 q^{78} - 2770 q^{79} - 3840 q^{80} - 25464 q^{81} - 17472 q^{82} - 36900 q^{83} - 24480 q^{84} - 24750 q^{85} + 624 q^{86} - 5760 q^{88} + 46596 q^{89} + 55360 q^{90} + 32370 q^{91} + 14112 q^{92} + 20722 q^{93} + 58880 q^{94} + 74250 q^{95} - 3732 q^{97} + 45802 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9 - 30 * q^11 - 384 * q^12 - 510 * q^13 - 96 * q^14 - 1398 * q^15 - 256 * q^16 + 1770 * q^17 + 1120 * q^18 + 1020 * q^19 - 240 * q^20 + 240 * q^22 - 2424 * q^23 - 640 * q^24 - 858 * q^25 + 480 * q^26 + 2224 * q^27 + 1600 * q^28 + 4890 * q^29 + 3360 * q^30 + 602 * q^31 - 2648 * q^33 - 3904 * q^34 - 8670 * q^35 + 720 * q^36 - 4518 * q^37 - 4800 * q^38 - 1130 * q^39 - 1280 * q^40 + 1290 * q^41 - 3808 * q^42 + 720 * q^44 + 12152 * q^45 + 4480 * q^46 + 642 * q^47 - 128 * q^48 + 9534 * q^49 + 6720 * q^50 - 1500 * q^51 + 4000 * q^52 + 2598 * q^53 + 2582 * q^55 - 3072 * q^56 + 9140 * q^57 - 6496 * q^58 + 6660 * q^59 - 5776 * q^60 - 27410 * q^61 - 19680 * q^62 - 27260 * q^63 + 2048 * q^64 + 2528 * q^66 + 21524 * q^67 + 14160 * q^68 + 11416 * q^69 + 34400 * q^70 - 5562 * q^71 + 10240 * q^72 - 7790 * q^73 + 5760 * q^74 + 3576 * q^75 - 1110 * q^77 - 39424 * q^78 - 2770 * q^79 - 3840 * q^80 - 25464 * q^81 - 17472 * q^82 - 36900 * q^83 - 24480 * q^84 - 24750 * q^85 + 624 * q^86 - 5760 * q^88 + 46596 * q^89 + 55360 * q^90 + 32370 * q^91 + 14112 * q^92 + 20722 * q^93 + 58880 * q^94 + 74250 * q^95 - 3732 * q^97 + 45802 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.68999	+	0.874032i	−0.672499	+	0.218508i
$2$	−2.68999	+	0.874032i	−0.672499	+	0.218508i
$3$	−3.20187	−	2.32629i	−0.355763	−	0.258477i	0.395520	−	0.918458i	$-0.370565\pi$
$3$	−3.20187	−	2.32629i	−0.355763	−	0.258477i	−0.751283	+	0.659980i	$0.770565\pi$
$4$	6.47214	−	4.70228i	0.404508	−	0.293893i
$5$	13.3838	−	41.1910i	0.535350	−	1.64764i	−0.207540	−	0.978226i	$-0.566546\pi$
$5$	13.3838	−	41.1910i	0.535350	−	1.64764i	0.742891	−	0.669413i	$-0.233454\pi$
$6$	10.6463	+	3.45918i	0.295729	+	0.0960883i
$7$	−7.80030	−	10.7362i	−0.159190	−	0.219106i	0.721970	−	0.691924i	$-0.243237\pi$
$7$	−7.80030	−	10.7362i	−0.159190	−	0.219106i	−0.881160	+	0.472818i	$0.843237\pi$
$8$	−13.3001	+	18.3060i	−0.207813	+	0.286031i
$9$	−20.1901	−	62.1386i	−0.249260	−	0.767143i
$10$			122.501i			1.22501i
$11$	90.5882	+	80.2170i	0.748663	+	0.662951i
$11$	90.5882	+	80.2170i	0.748663	+	0.662951i
$12$	−31.6618			−0.219874
$13$	−170.407	+	55.3685i	−1.00832	+	0.327624i	−0.766187	−	0.642618i	$-0.777848\pi$
$13$	−170.407	+	55.3685i	−1.00832	+	0.327624i	−0.242137	+	0.970242i	$0.577848\pi$
$14$	30.3665	+	22.0626i	0.154931	+	0.112564i
$15$	−138.675	+	100.754i	−0.616335	+	0.447794i
$16$	19.7771	−	60.8676i	0.0772542	−	0.237764i
$17$	167.901	+	54.5543i	0.580972	+	0.188769i	0.584736	−	0.811224i	$-0.301198\pi$
$17$	167.901	+	54.5543i	0.580972	+	0.188769i	−0.00376408	+	0.999993i	$0.501198\pi$
$18$	108.622	+	149.506i	0.335254	+	0.461437i
$19$	213.240	−	293.500i	0.590693	−	0.813019i	−0.404123	−	0.914704i	$-0.632423\pi$
$19$	213.240	−	293.500i	0.590693	−	0.813019i	0.994817	+	0.101685i	$0.0324234\pi$
$20$	−107.070	−	329.528i	−0.267675	−	0.823820i
$21$			52.5217i			0.119097i
$22$	−313.794	−	136.606i	−0.648335	−	0.282244i
$23$	564.946			1.06795			0.533975	−	0.845500i	$-0.320698\pi$
$23$	564.946			1.06795			0.533975	+	0.845500i	$0.320698\pi$
$24$	85.1701	−	27.6734i	0.147865	−	0.0480442i
$25$	−1011.94	−	735.215i	−1.61910	−	1.17634i
$26$	409.999	−	297.882i	0.606508	−	0.440654i
$27$	−178.970	+	550.813i	−0.245501	+	0.755574i
$28$	−100.969	−	32.8069i	−0.128787	−	0.0418455i
$29$	505.658	+	695.978i	0.601258	+	0.827560i	0.995823	−	0.0913079i	$-0.0291048\pi$
$29$	505.658	+	695.978i	0.601258	+	0.827560i	−0.394565	+	0.918868i	$0.629105\pi$
$30$	284.974	−	392.233i	0.316638	−	0.435815i
$31$	276.141	+	849.875i	0.287348	+	0.884365i	0.985685	+	0.168596i	$0.0539234\pi$
$31$	276.141	+	849.875i	0.287348	+	0.884365i	−0.698338	+	0.715769i	$0.746077\pi$
$32$			181.019i			0.176777i
$33$	−103.443	−	467.579i	−0.0949893	−	0.429366i
$34$	−499.334			−0.431950
$35$	−546.632	+	177.611i	−0.446230	+	0.144989i
$36$	−422.866	−	307.230i	−0.326286	−	0.237060i
$37$	−164.418	+	119.457i	−0.120101	+	0.0872585i	−0.646214	−	0.763156i	$-0.723649\pi$
$37$	−164.418	+	119.457i	−0.120101	+	0.0872585i	0.526113	+	0.850415i	$0.323649\pi$
$38$	−317.087	+	975.892i	−0.219589	+	0.675826i
$39$	674.423	+	219.133i	0.443408	+	0.144072i
$40$	576.036	+	792.845i	0.360022	+	0.495528i
$41$	1540.12	−	2119.80i	0.916196	−	1.26103i	−0.0488107	−	0.998808i	$-0.515543\pi$
$41$	1540.12	−	2119.80i	0.916196	−	1.26103i	0.965006	−	0.262227i	$-0.0844569\pi$
$42$	−45.9056	−	141.283i	−0.0260236	−	0.0800924i
$43$			2603.62i			1.40812i	0.710140	+	0.704061i	$0.248632\pi$
$43$			2603.62i			1.40812i	−0.710140	+	0.704061i	$0.751368\pi$
$44$	963.502	+	93.2040i	0.497677	+	0.0481425i
$45$	−2829.77			−1.39742
$46$	−1519.70	+	493.780i	−0.718195	+	0.233356i
$47$	−1250.87	−	908.812i	−0.566262	−	0.411413i	0.267484	−	0.963562i	$-0.413808\pi$
$47$	−1250.87	−	908.812i	−0.566262	−	0.411413i	−0.833745	+	0.552149i	$0.813808\pi$
$48$	−204.920	+	148.883i	−0.0889408	+	0.0646193i
$49$	687.529	−	2116.00i	0.286351	−	0.881298i
$50$	3364.70	+	1093.26i	1.34588	+	0.437303i
$51$	−410.687	−	565.262i	−0.157896	−	0.217325i
$52$	−842.537	+	1159.65i	−0.311589	+	0.428866i
$53$	−454.551	−	1398.97i	−0.161820	−	0.498030i	0.836968	−	0.547251i	$-0.184326\pi$
$53$	−454.551	−	1398.97i	−0.161820	−	0.498030i	−0.998788	+	0.0492218i	$0.984326\pi$
$54$		−	1638.11i		−	0.561766i
$55$	4516.63	−	2657.81i	1.49310	−	0.878616i
$56$	300.281			0.0957528
$57$	−1365.53	+	443.689i	−0.420294	+	0.136562i
$58$	−1968.52	−	1430.22i	−0.585173	−	0.425153i
$59$	3977.33	−	2889.70i	1.14258	−	0.830135i	0.155106	−	0.987898i	$-0.450428\pi$
$59$	3977.33	−	2889.70i	1.14258	−	0.830135i	0.987477	+	0.157762i	$0.0504280\pi$
$60$	−423.754	+	1304.18i	−0.117709	+	0.362273i
$61$	−1508.75	−	490.221i	−0.405468	−	0.131745i	0.0991805	−	0.995069i	$-0.468378\pi$
$61$	−1508.75	−	490.221i	−0.405468	−	0.131745i	−0.504648	+	0.863325i	$0.668378\pi$
$62$	−1485.64	−	2044.80i	−0.386482	−	0.531946i
$63$	−509.644	+	701.464i	−0.128406	+	0.176736i
$64$	−158.217	−	486.941i	−0.0386271	−	0.118882i
$65$			7760.26i			1.83675i
$66$	686.941	+	1167.37i	0.157700	+	0.267992i
$67$	−3004.99			−0.669413			−0.334706	−	0.942323i	$-0.608637\pi$
$67$	−3004.99			−0.669413			−0.334706	+	0.942323i	$0.608637\pi$
$68$	1343.21	−	436.434i	0.290486	−	0.0943846i
$69$	−1808.88	−	1314.23i	−0.379937	−	0.276041i
$70$	1315.20	−	955.547i	0.268408	−	0.195010i
$71$	−2625.89	+	8081.67i	−0.520907	+	1.60319i	0.251362	+	0.967893i	$0.419121\pi$
$71$	−2625.89	+	8081.67i	−0.520907	+	1.60319i	−0.772270	+	0.635295i	$0.780879\pi$
$72$	1406.04	+	456.849i	0.271226	+	0.0881267i
$73$	2674.58	+	3681.24i	0.501891	+	0.690793i	0.982526	−	0.186127i	$-0.0595937\pi$
$73$	2674.58	+	3681.24i	0.501891	+	0.690793i	−0.480635	+	0.876921i	$0.659594\pi$
$74$	337.875	−	465.045i	0.0617011	−	0.0849243i
$75$	1529.76	+	4708.12i	0.271958	+	0.836999i
$76$		−	2902.29i		−	0.502474i
$77$	154.610	−	1598.29i	0.0260769	−	0.269572i
$78$	−2005.72			−0.329672
$79$	2009.88	−	653.050i	0.322045	−	0.104639i	−0.143533	−	0.989645i	$-0.545846\pi$
$79$	2009.88	−	653.050i	0.322045	−	0.104639i	0.465578	+	0.885007i	$0.345846\pi$
$80$	−2242.51	−	1629.28i	−0.350391	−	0.254574i
$81$	−2427.13	+	1763.41i	−0.369932	+	0.268772i
$82$	−2290.15	+	7048.37i	−0.340594	+	1.04824i
$83$	−8994.67	−	2922.55i	−1.30566	−	0.424234i	−0.428111	−	0.903726i	$-0.640821\pi$
$83$	−8994.67	−	2922.55i	−1.30566	−	0.424234i	−0.877546	+	0.479493i	$0.840821\pi$
$84$	246.972	+	339.927i	0.0350016	+	0.0481756i
$85$	4494.29	−	6185.86i	0.622047	−	0.856174i
$86$	−2275.65	−	7003.72i	−0.307686	−	0.946960i
$87$		−	3404.74i		−	0.449827i
$88$	−2673.28	+	591.414i	−0.345207	+	0.0763706i
$89$	14557.2			1.83779			0.918896	−	0.394499i	$-0.129082\pi$
$89$	14557.2			1.83779			0.918896	+	0.394499i	$0.129082\pi$
$90$	7612.06	−	2473.31i	0.939761	−	0.305347i
$91$	1923.67	+	1397.63i	0.232299	+	0.168775i
$92$	3656.40	−	2656.53i	0.431995	−	0.313863i
$93$	1092.89	−	3363.57i	0.126360	−	0.388897i
$94$	4159.17	+	1351.40i	0.470707	+	0.152942i
$95$	−9235.60	−	12711.7i	−1.02333	−	1.40850i
$96$	421.104	−	579.600i	0.0456927	−	0.0628906i
$97$	2097.12	+	6454.28i	0.222885	+	0.685969i	0.998499	+	0.0547624i	$0.0174401\pi$
$97$	2097.12	+	6454.28i	0.222885	+	0.685969i	−0.775614	+	0.631207i	$0.782560\pi$
$98$			6292.94i			0.655241i
$99$	3155.59	−	7248.61i	0.321966	−	0.739579i
$100$	−10006.6			−1.00066
$101$	−12997.2	+	4223.06i	−1.27411	+	0.413985i	−0.866504	−	0.499171i	$-0.833638\pi$
$101$	−12997.2	+	4223.06i	−1.27411	+	0.413985i	−0.407611	+	0.913156i	$0.633638\pi$
$102$	1598.80	+	1161.60i	0.153672	+	0.111649i
$103$	−995.164	+	723.029i	−0.0938038	+	0.0681524i	−0.633699	−	0.773580i	$-0.718464\pi$
$103$	−995.164	+	723.029i	−0.0938038	+	0.0681524i	0.539895	+	0.841733i	$0.318464\pi$
$104$	1252.85	−	3855.86i	0.115833	−	0.356496i
$105$	2163.42	+	702.937i	0.196228	+	0.0637585i
$106$	2445.48	+	3365.92i	0.217647	+	0.299565i
$107$	−4974.60	+	6846.95i	−0.434501	+	0.598040i	−0.968979	−	0.247143i	$-0.920508\pi$
$107$	−4974.60	+	6846.95i	−0.434501	+	0.598040i	0.534478	+	0.845182i	$0.320508\pi$
$108$	1431.76	+	4406.51i	0.122750	+	0.377787i
$109$		−	7648.65i		−	0.643771i	−0.946779	−	0.321886i	$-0.895683\pi$
$109$		−	7648.65i		−	0.643771i	0.946779	−	0.321886i	$-0.104317\pi$
$110$	−9826.69	+	11097.2i	−0.812123	+	0.917122i
$111$	804.338			0.0652819
$112$	−807.754	+	262.455i	−0.0643936	+	0.0209228i
$113$	7345.60	+	5336.89i	0.575269	+	0.417957i	0.837015	−	0.547180i	$-0.184298\pi$
$113$	7345.60	+	5336.89i	0.575269	+	0.417957i	−0.261747	+	0.965137i	$0.584298\pi$
$114$	3285.48	−	2387.04i	0.252807	−	0.183675i
$115$	7561.10	−	23270.7i	0.571728	−	1.75960i
$116$	6545.37	+	2126.72i	0.486428	+	0.158050i
$117$	6881.04	+	9470.94i	0.502670	+	0.691865i
$118$	−8173.31	+	11249.6i	−0.586994	+	0.807928i
$119$	−723.972	−	2228.16i	−0.0511243	−	0.157345i
$120$		−	3878.61i		−	0.269348i
$121$	1771.46	+	14533.4i	0.120993	+	0.992653i
$122$	4486.99			0.301464
$123$	−9862.55	+	3204.54i	−0.651897	+	0.211814i
$124$	5783.57	+	4202.01i	0.376143	+	0.273284i
$125$	−21928.3	+	15931.8i	−1.40341	+	1.01964i
$126$	757.836	−	2332.38i	0.0477347	−	0.146912i
$127$	−6550.78	−	2128.48i	−0.406149	−	0.131966i	0.0988156	−	0.995106i	$-0.468495\pi$
$127$	−6550.78	−	2128.48i	−0.406149	−	0.131966i	−0.504965	+	0.863140i	$0.668495\pi$
$128$	851.204	+	1171.58i	0.0519534	+	0.0715077i
$129$	6056.78	−	8336.44i	0.363967	−	0.500958i
$130$	−6782.72	−	20875.1i	−0.401344	−	1.23521i
$131$			1471.01i			0.0857182i	0.999081	+	0.0428591i	$0.0136467\pi$
$131$			1471.01i			0.0857182i	−0.999081	+	0.0428591i	$0.986353\pi$
$132$	−2868.19	−	2539.82i	−0.164611	−	0.145765i
$133$	−4814.41			−0.272170
$134$	8083.41	−	2626.46i	0.450179	−	0.146272i
$135$	20293.3	+	14743.9i	1.11348	+	0.808994i
$136$	−3231.76	+	2348.01i	−0.174728	+	0.126947i
$137$	5600.55	−	17236.7i	0.298394	−	0.918361i	−0.683667	−	0.729794i	$-0.739616\pi$
$137$	5600.55	−	17236.7i	0.298394	−	0.918361i	0.982060	−	0.188567i	$-0.0603841\pi$
$138$	6014.56	+	1954.25i	0.315824	+	0.102618i
$139$	5984.50	+	8236.96i	0.309741	+	0.426322i	0.935300	−	0.353855i	$-0.115129\pi$
$139$	5984.50	+	8236.96i	0.309741	+	0.426322i	−0.625559	+	0.780176i	$0.715129\pi$
$140$	−2702.70	+	3719.94i	−0.137893	+	0.189793i
$141$	1890.97	+	5819.79i	0.0951142	+	0.292731i
$142$		−	24034.8i		−	1.19196i
$143$	−19878.3	−	8653.78i	−0.972094	−	0.423189i
$144$	−4181.53			−0.201656
$145$	35435.6	−	11513.7i	1.68540	−	0.547621i
$146$	−10412.1	−	7564.84i	−0.488465	−	0.354890i
$147$	−7123.80	+	5175.75i	−0.329668	+	0.239518i
$148$	−502.418	+	1546.28i	−0.0229373	+	0.0705936i
$149$	−25251.0	−	8204.56i	−1.13738	−	0.369558i	−0.321006	−	0.947077i	$-0.604021\pi$
$149$	−25251.0	−	8204.56i	−1.13738	−	0.369558i	−0.816377	+	0.577519i	$0.804021\pi$
$150$	−8230.10	−	11327.8i	−0.365782	−	0.503456i
$151$	−11161.2	+	15362.0i	−0.489503	+	0.673744i	−0.980296	−	0.197533i	$-0.936707\pi$
$151$	−11161.2	+	15362.0i	−0.489503	+	0.673744i	0.490793	+	0.871276i	$0.336707\pi$
$152$	2536.69	+	7807.14i	0.109795	+	0.337913i
$153$		−	11534.6i		−	0.492741i
$154$	981.057	+	4434.52i	0.0413669	+	0.186984i
$155$	38703.0			1.61095
$156$	5395.39	−	1753.07i	0.221704	−	0.0720360i
$157$	2755.25	+	2001.81i	0.111779	+	0.0812124i	0.642271	−	0.766478i	$-0.277993\pi$
$157$	2755.25	+	2001.81i	0.111779	+	0.0812124i	−0.530491	+	0.847690i	$0.677993\pi$
$158$	−4835.78	+	3513.40i	−0.193710	+	0.140739i
$159$	−1798.99	+	5536.72i	−0.0711598	+	0.219007i
$160$	7456.36	+	2422.72i	0.291264	+	0.0946375i
$161$	−4406.74	−	6065.36i	−0.170007	−	0.233994i
$162$	4987.68	−	6864.95i	0.190050	−	0.261582i
$163$	2632.77	+	8102.84i	0.0990918	+	0.304973i	0.988298	−	0.152533i	$-0.0487429\pi$
$163$	2632.77	+	8102.84i	0.0990918	+	0.304973i	−0.889207	+	0.457506i	$0.848743\pi$
$164$		−	20961.7i		−	0.779362i
$165$	−20644.5	−	1997.04i	−0.758292	−	0.0733530i
$166$	26750.0			0.970751
$167$	12611.3	−	4097.65i	0.452196	−	0.146927i	−0.0740598	−	0.997254i	$-0.523596\pi$
$167$	12611.3	−	4097.65i	0.452196	−	0.146927i	0.526255	+	0.850327i	$0.323596\pi$
$168$	−961.460	−	698.541i	−0.0340653	−	0.0247499i
$169$	2866.45	−	2082.59i	0.100362	−	0.0729174i
$170$	−6682.97	+	20568.1i	−0.231245	+	0.711698i
$171$	−22543.0	−	7324.67i	−0.770939	−	0.250493i
$172$	12242.9	+	16851.0i	0.413837	+	0.569597i
$173$	−12984.4	+	17871.4i	−0.433839	+	0.597128i	−0.968829	−	0.247730i	$-0.920315\pi$
$173$	−12984.4	+	17871.4i	−0.433839	+	0.597128i	0.534990	+	0.844858i	$0.320315\pi$
$174$	2975.85	+	9158.72i	0.0982907	+	0.302508i
$175$			16599.2i			0.542016i
$176$	6674.19	−	3927.43i	0.215463	−	0.126790i
$177$	−19457.2			−0.621060
$178$	−39158.7	+	12723.4i	−1.23591	+	0.401572i
$179$	6760.86	+	4912.05i	0.211006	+	0.153305i	0.688269	−	0.725456i	$-0.258371\pi$
$179$	6760.86	+	4912.05i	0.211006	+	0.153305i	−0.477263	+	0.878761i	$0.658371\pi$
$180$	−18314.7	+	13306.4i	−0.565267	+	0.410691i
$181$	3111.80	−	9577.13i	0.0949848	−	0.292333i	−0.892265	−	0.451512i	$-0.850885\pi$
$181$	3111.80	−	9577.13i	0.0949848	−	0.292333i	0.987250	+	0.159179i	$0.0508847\pi$
$182$	−6396.23	−	2078.26i	−0.193100	−	0.0627419i
$183$	3690.41	+	5079.41i	0.110198	+	0.151674i
$184$	−7513.81	+	10341.9i	−0.221934	+	0.305466i
$185$	2720.01	+	8371.34i	0.0794744	+	0.244597i
$186$			10003.2i			0.289144i
$187$	10833.7	+	18410.5i	0.309808	+	0.526480i
$188$	−12369.3			−0.349969
$189$	7309.66	−	2375.05i	0.204632	−	0.0664890i
$190$	35954.1	+	26122.2i	0.995960	+	0.723607i
$191$	28569.5	−	20757.0i	0.783134	−	0.568980i	−0.122784	−	0.992433i	$-0.539182\pi$
$191$	28569.5	−	20757.0i	0.783134	−	0.568980i	0.905918	+	0.423453i	$0.139182\pi$
$192$	−626.178	+	1927.18i	−0.0169862	+	0.0522781i
$193$	−7441.19	−	2417.79i	−0.199769	−	0.0649088i	0.207424	−	0.978251i	$-0.433492\pi$
$193$	−7441.19	−	2417.79i	−0.199769	−	0.0649088i	−0.407192	+	0.913342i	$0.633492\pi$
$194$	−11282.5	−	15529.0i	−0.299780	−	0.412611i
$195$	18052.6	−	24847.3i	0.474757	−	0.653447i
$196$	−5500.23	−	16928.0i	−0.143175	−	0.440649i
$197$			1473.23i			0.0379610i	0.999820	+	0.0189805i	$0.00604205\pi$
$197$			1473.23i			0.0379610i	−0.999820	+	0.0189805i	$0.993958\pi$
$198$	−2153.00	+	22256.8i	−0.0549179	+	0.567718i
$199$	−26096.6			−0.658987			−0.329494	−	0.944158i	$-0.606878\pi$
$199$	−26096.6			−0.658987			−0.329494	+	0.944158i	$0.606878\pi$
$200$	26917.6	−	8746.07i	0.672941	−	0.218652i
$201$	9621.59	+	6990.49i	0.238152	+	0.173028i
$202$	31271.4	−	22720.0i	0.766381	−	0.556809i
$203$	3527.87	−	10857.7i	0.0856093	−	0.263478i
$204$	−5316.05	−	1727.29i	−0.127740	−	0.0415054i
$205$	−66704.0	−	91810.1i	−1.58725	−	2.18466i
$206$	2045.04	−	2814.75i	0.0481910	−	0.0663293i
$207$	−11406.3	−	35104.9i	−0.266197	−	0.819271i
$208$			11467.3i			0.265054i
$209$	42860.8	−	9482.15i	0.981222	−	0.217077i
$210$	−6433.97			−0.145895
$211$	−68859.0	+	22373.6i	−1.54666	+	0.502541i	−0.953205	−	0.302323i	$-0.902238\pi$
$211$	−68859.0	+	22373.6i	−1.54666	+	0.502541i	−0.593458	+	0.804865i	$0.702238\pi$
$212$	−9520.25	−	6916.86i	−0.211825	−	0.153900i
$213$	27208.1	−	19767.8i	0.599707	−	0.435713i
$214$	7397.20	−	22766.2i	0.161525	−	0.497123i
$215$	107246.	+	34846.2i	2.32008	+	0.753839i
$216$	−7702.86	−	10602.1i	−0.165099	−	0.227239i
$217$	6970.43	−	9593.98i	0.148027	−	0.203741i
$218$	6685.16	+	20574.8i	0.140669	+	0.432935i
$219$		−	18008.7i		−	0.375486i
$220$	16734.5	−	38440.2i	0.345753	−	0.794219i
$221$	−31632.0			−0.647653
$222$	−2163.66	+	703.017i	−0.0439020	+	0.0142646i
$223$	−22887.6	−	16628.8i	−0.460246	−	0.334388i	0.333382	−	0.942792i	$-0.391810\pi$
$223$	−22887.6	−	16628.8i	−0.460246	−	0.334388i	−0.793628	+	0.608404i	$0.791810\pi$
$224$	1943.46	−	1412.01i	0.0387328	−	0.0281410i
$225$	−25254.2	+	77724.3i	−0.498848	+	1.53530i
$226$	−24424.2	−	7935.92i	−0.478194	−	0.155375i
$227$	42352.4	+	58293.1i	0.821913	+	1.13127i	0.989375	+	0.145388i	$0.0464431\pi$
$227$	42352.4	+	58293.1i	0.821913	+	1.13127i	−0.167461	+	0.985879i	$0.553557\pi$
$228$	−6751.57	+	9292.74i	−0.129878	+	0.178762i
$229$	2762.09	+	8500.84i	0.0526704	+	0.162103i	0.973932	−	0.226841i	$-0.0728399\pi$
$229$	2762.09	+	8500.84i	0.0526704	+	0.162103i	−0.921261	+	0.388944i	$0.872840\pi$
$230$			69206.6i			1.30825i
$231$	−4213.13	+	4757.84i	−0.0789552	+	0.0891633i
$232$	−19465.8			−0.361657
$233$	46046.9	−	14961.6i	0.848182	−	0.275591i	0.147497	−	0.989062i	$-0.452878\pi$
$233$	46046.9	−	14961.6i	0.848182	−	0.275591i	0.700684	+	0.713472i	$0.252878\pi$
$234$	−26787.9	−	19462.5i	−0.489223	−	0.355441i
$235$	−54176.2	+	39361.3i	−0.981009	+	0.712745i
$236$	12153.6	−	37405.1i	0.218214	−	0.671594i
$237$	−7954.57	−	2584.59i	−0.141618	−	0.0460146i
$238$	3894.96	+	5360.95i	0.0687621	+	0.0946429i
$239$	−31831.6	+	43812.5i	−0.557266	+	0.767011i	−0.990976	−	0.134041i	$-0.957204\pi$
$239$	−31831.6	+	43812.5i	−0.557266	+	0.767011i	0.433709	+	0.901053i	$0.357204\pi$
$240$	3390.03	+	10433.4i	0.0588547	+	0.181136i
$241$			54166.9i			0.932610i	0.884624	+	0.466305i	$0.154415\pi$
$241$			54166.9i			0.932610i	−0.884624	+	0.466305i	$0.845585\pi$
$242$	−17467.9	−	37546.5i	−0.298270	−	0.641120i
$243$	58785.5			0.995537
$244$	−12070.0	+	3921.77i	−0.202734	+	0.0658723i
$245$	−77958.2	−	56640.0i	−1.29876	−	0.943606i
$246$	23729.3	−	17240.4i	0.392117	−	0.284890i
$247$	−20086.9	+	61821.2i	−0.329245	+	1.01331i
$248$	−19230.5	−	6248.36i	−0.312670	−	0.101593i
$249$	22001.0	+	30281.8i	0.354850	+	0.488409i
$250$	45062.0	−	62022.5i	0.720992	−	0.992360i
$251$	4416.42	+	13592.3i	0.0701008	+	0.215748i	0.979969	−	0.199149i	$-0.0638177\pi$
$251$	4416.42	+	13592.3i	0.0701008	+	0.215748i	−0.909868	+	0.414897i	$0.863818\pi$
$252$			6936.46i			0.109229i
$253$	51177.4	+	45318.2i	0.799535	+	0.707998i
$254$	19481.9			0.301970
$255$	−28780.2	+	9351.27i	−0.442603	+	0.143810i
$256$	−3313.73	−	2407.57i	−0.0505636	−	0.0367366i
$257$	31133.7	−	22619.9i	0.471372	−	0.342472i	−0.326604	−	0.945161i	$-0.605904\pi$
$257$	31133.7	−	22619.9i	0.471372	−	0.342472i	0.797976	+	0.602689i	$0.205904\pi$
$258$	−9006.38	+	27718.8i	−0.135304	+	0.416423i
$259$	2565.02	+	833.427i	0.0382377	+	0.0124242i
$260$	36490.9	+	50225.5i	0.539807	+	0.742980i
$261$	33037.8	−	45472.7i	0.484988	−	0.667528i
$262$	−1285.71	−	3957.01i	−0.0187301	−	0.0576454i
$263$		−	130054.i		−	1.88024i	−0.340841	−	0.940121i	$-0.610712\pi$
$263$		−	130054.i		−	1.88024i	0.340841	−	0.940121i	$-0.389288\pi$
$264$	9935.29	+	4325.20i	0.142552	+	0.0620581i
$265$	−63708.4			−0.907203
$266$	12950.7	−	4207.95i	0.183034	−	0.0594713i
$267$	−46610.1	−	33864.2i	−0.653819	−	0.475027i
$268$	−19448.7	+	14130.3i	−0.270783	+	0.196735i
$269$	−21831.7	+	67190.9i	−0.301705	+	0.928552i	0.679182	+	0.733970i	$0.262335\pi$
$269$	−21831.7	+	67190.9i	−0.301705	+	0.928552i	−0.980886	+	0.194582i	$0.937665\pi$
$270$	−67475.4	−	21924.1i	−0.925588	−	0.300742i
$271$	46867.1	+	64507.0i	0.638160	+	0.878352i	0.998516	−	0.0544632i	$-0.0173448\pi$
$271$	46867.1	+	64507.0i	0.638160	+	0.878352i	−0.360356	+	0.932815i	$0.617345\pi$
$272$	6641.18	−	9140.80i	0.0897651	−	0.123551i
$273$	−2908.05	−	8950.04i	−0.0390190	−	0.120088i
$274$			51261.7i			0.682798i
$275$	−32692.8	−	147776.i	−0.432301	−	1.95407i
$276$	−17887.2			−0.234814
$277$	42143.0	−	13693.1i	0.549245	−	0.178461i	−0.0212312	−	0.999775i	$-0.506759\pi$
$277$	42143.0	−	13693.1i	0.549245	−	0.178461i	0.570476	+	0.821314i	$0.306759\pi$
$278$	−23297.7	−	16926.7i	−0.301455	−	0.219020i
$279$	47234.7	−	34318.0i	0.606810	−	0.440874i
$280$	4018.89	−	12368.9i	0.0512613	−	0.157766i
$281$	74439.7	+	24186.9i	0.942740	+	0.306315i	0.739762	−	0.672868i	$-0.234938\pi$
$281$	74439.7	+	24186.9i	0.942740	+	0.306315i	0.202978	+	0.979183i	$0.434938\pi$
$282$	−10173.4	−	14002.4i	−0.127928	−	0.176078i
$283$	52782.1	−	72648.4i	0.659043	−	0.907095i	−0.340406	−	0.940279i	$-0.610564\pi$
$283$	52782.1	−	72648.4i	0.659043	−	0.907095i	0.999449	+	0.0331832i	$0.0105645\pi$
$284$	21007.2	+	64653.4i	0.260454	+	0.801594i
$285$			62185.9i			0.765601i
$286$	61036.3	+	5904.32i	0.746202	+	0.0721835i
$287$	−34772.0			−0.422149
$288$	11248.3	−	3654.79i	0.135613	−	0.0440634i
$289$	−42355.4	−	30773.0i	−0.507123	−	0.368446i
$290$	−85258.2	+	61943.7i	−1.01377	+	0.736549i
$291$	8299.84	−	25544.3i	0.0980131	−	0.301653i
$292$	34620.4	+	11248.9i	0.406038	+	0.131930i
$293$	12058.9	+	16597.6i	0.140466	+	0.193335i	0.873454	−	0.486907i	$-0.161875\pi$
$293$	12058.9	+	16597.6i	0.140466	+	0.193335i	−0.732988	+	0.680242i	$0.761875\pi$
$294$	14639.2	−	20149.2i	0.169365	−	0.233111i
$295$	−65798.0	−	202505.i	−0.756081	−	2.32698i
$296$		−	4598.62i		−	0.0524861i
$297$	−60397.2	+	35540.8i	−0.684706	+	0.402915i
$298$	75096.2			0.845640
$299$	−96270.5	+	31280.2i	−1.07684	+	0.349886i
$300$	32039.7	+	23278.2i	0.355997	+	0.258647i
$301$	27952.9	−	20309.0i	0.308528	−	0.224159i
$302$	16596.6	−	51079.0i	0.181972	−	0.560052i
$303$	51439.5	+	16713.7i	0.560289	+	0.182049i
$304$	−13647.4	−	18784.0i	−0.147673	−	0.203255i
$305$	−40385.4	+	55585.7i	−0.434135	+	0.597535i
$306$	10081.6	+	31028.0i	0.107668	+	0.331368i
$307$			133825.i			1.41991i	0.704248	+	0.709954i	$0.251284\pi$
$307$			133825.i			1.41991i	−0.704248	+	0.709954i	$0.748716\pi$
$308$	−6514.95	−	11071.4i	−0.0686768	−	0.116708i
$309$	4868.36			0.0509878
$310$	−104111.	+	33827.6i	−1.08336	+	0.352005i
$311$	−34207.5	−	24853.2i	−0.353672	−	0.256958i	0.396736	−	0.917933i	$-0.370143\pi$
$311$	−34207.5	−	24853.2i	−0.353672	−	0.256958i	−0.750408	+	0.660975i	$0.770143\pi$
$312$	−12981.3	+	9431.48i	−0.133355	+	0.0968882i
$313$	53394.1	−	164330.i	0.545011	−	1.67737i	−0.175954	−	0.984398i	$-0.556301\pi$
$313$	53394.1	−	164330.i	0.545011	−	1.67737i	0.720965	−	0.692972i	$-0.243699\pi$
$314$	−9161.25	−	2976.67i	−0.0929170	−	0.0301906i
$315$	22073.0	+	30380.9i	0.222455	+	0.306182i
$316$	9937.41	−	13677.7i	0.0995174	−	0.136974i
$317$	26059.8	+	80203.7i	0.259329	+	0.798134i	0.992946	+	0.118570i	$0.0378310\pi$
$317$	26059.8	+	80203.7i	0.259329	+	0.798134i	−0.733616	+	0.679564i	$0.762169\pi$
$318$		−	16466.1i		−	0.162831i
$319$	−10022.6	+	103610.i	−0.0984920	+	1.01817i
$320$	−22175.1			−0.216554
$321$	31856.1	−	10350.7i	0.309159	−	0.100452i
$322$	17155.4	+	12464.2i	0.165459	+	0.120213i
$323$	51814.9	−	37645.7i	0.496649	−	0.360837i
$324$	−7416.64	+	22826.1i	−0.0706508	+	0.217441i
$325$	213149.	+	69256.1i	2.01797	+	0.655679i
$326$	−14164.3	−	19495.5i	−0.133278	−	0.183442i
$327$	−17793.0	+	24490.0i	−0.166400	+	0.229030i
$328$	18321.2	+	56386.9i	0.170297	+	0.524120i
$329$			20518.6i			0.189564i
$330$	57279.1	−	12671.9i	0.525979	−	0.116363i
$331$	−130067.			−1.18717			−0.593583	−	0.804773i	$-0.702287\pi$
$331$	−130067.			−1.18717			−0.593583	+	0.804773i	$0.702287\pi$
$332$	−71957.4	+	23380.4i	−0.652828	+	0.212117i
$333$	10742.5	+	7804.89i	0.0968762	+	0.0703847i
$334$	−30342.8	+	22045.3i	−0.271996	+	0.197617i
$335$	−40218.1	+	123779.i	−0.358370	+	1.10295i
$336$	3196.87	+	1038.73i	0.0283169	+	0.00920073i
$337$	−48084.9	−	66183.1i	−0.423398	−	0.582757i	0.543024	−	0.839717i	$-0.317279\pi$
$337$	−48084.9	−	66183.1i	−0.423398	−	0.582757i	−0.966422	+	0.256960i	$0.917279\pi$
$338$	−5890.47	+	8107.53i	−0.0515604	+	0.0709668i
$339$	−11104.5	−	34176.1i	−0.0966270	−	0.297387i
$340$		−	61169.1i		−	0.529145i
$341$	−43159.3	+	99139.9i	−0.371164	+	0.852589i
$342$	67042.6			0.573190
$343$	−58384.0	+	18970.1i	−0.496256	+	0.161243i
$344$	−47661.7	−	34628.3i	−0.402766	−	0.292627i
$345$	−78344.0	+	56920.3i	−0.658215	+	0.478221i
$346$	19307.6	−	59422.8i	0.161279	−	0.496365i
$347$	−219762.	−	71404.9i	−1.82513	−	0.593019i	−0.999589	−	0.0286715i	$-0.990872\pi$
$347$	−219762.	−	71404.9i	−1.82513	−	0.593019i	−0.825537	−	0.564348i	$-0.809128\pi$
$348$	−16010.0	−	22035.9i	−0.132201	−	0.181959i
$349$	−7604.61	+	10466.9i	−0.0624347	+	0.0859340i	−0.839093	−	0.543989i	$-0.816913\pi$
$349$	−7604.61	+	10466.9i	−0.0624347	+	0.0859340i	0.776658	+	0.629923i	$0.216913\pi$
$350$	−14508.3	−	44651.9i	−0.118435	−	0.364505i
$351$		−	103772.i		−	0.842295i
$352$	−14520.8	+	16398.2i	−0.117194	+	0.132346i
$353$	59097.3			0.474262			0.237131	−	0.971478i	$-0.423793\pi$
$353$	59097.3			0.474262			0.237131	+	0.971478i	$0.423793\pi$
$354$	52339.7	−	17006.2i	0.417662	−	0.135707i
$355$	297748.	+	216326.i	2.36261	+	1.71654i
$356$	94215.9	−	68451.8i	0.743403	−	0.540114i
$357$	−2865.28	+	8818.43i	−0.0224818	+	0.0691918i
$358$	−22480.0	−	7304.18i	−0.175400	−	0.0569909i
$359$	−32828.5	−	45184.6i	−0.254720	−	0.350591i	0.662438	−	0.749117i	$-0.269522\pi$
$359$	−32828.5	−	45184.6i	−0.254720	−	0.350591i	−0.917157	+	0.398526i	$0.869522\pi$
$360$	37636.1	−	51801.7i	0.290402	−	0.399704i
$361$	−399.455	−	1229.40i	−0.00306517	−	0.00943361i
$362$			28482.2i			0.217349i
$363$	28137.1	−	50655.1i	0.213533	−	0.384423i
$364$	19022.3			0.143569
$365$	187430.	−	60899.6i	1.40687	−	0.457118i
$366$	−14366.7	−	10438.0i	−0.107250	−	0.0779215i
$367$	128062.	−	93042.3i	0.950796	−	0.690793i	−0.000199318	−	1.00000i	$-0.500063\pi$
$367$	128062.	−	93042.3i	0.950796	−	0.690793i	0.950995	+	0.309207i	$0.100063\pi$
$368$	11173.0	−	34386.9i	0.0825037	−	0.253920i
$369$	−162817.	−	52902.3i	−1.19577	−	0.388528i
$370$	−14633.6	−	20141.5i	−0.106893	−	0.147125i
$371$	−11473.9	+	15792.5i	−0.0833612	+	0.114737i
$372$	−8743.13	−	26908.6i	−0.0631802	−	0.194449i
$373$		−	133744.i		−	0.961297i	−0.876913	−	0.480649i	$-0.840401\pi$
$373$		−	133744.i		−	0.961297i	0.876913	−	0.480649i	$-0.159599\pi$
$374$	−45233.8	−	40055.1i	−0.323385	−	0.286362i
$375$	107274.			0.762834
$376$	33273.4	−	10811.2i	0.235354	−	0.0764710i
$377$	−124703.	−	90601.8i	−0.877391	−	0.637462i
$378$	−17587.1	+	12777.8i	−0.123086	+	0.0894274i
$379$	−16655.2	+	51259.4i	−0.115950	+	0.356858i	−0.992144	−	0.125101i	$-0.960075\pi$
$379$	−16655.2	+	51259.4i	−0.115950	+	0.356858i	0.876194	+	0.481959i	$0.160075\pi$
$380$	−119548.	−	38843.5i	−0.827895	−	0.269000i
$381$	16023.3	+	22054.1i	0.110383	+	0.151929i
$382$	−58709.6	+	80806.8i	−0.402330	+	0.553759i
$383$	15091.9	+	46448.1i	0.102884	+	0.316643i	0.989228	−	0.146383i	$-0.0467633\pi$
$383$	15091.9	+	46448.1i	0.102884	+	0.316643i	−0.886344	+	0.463027i	$0.846763\pi$
$384$		−	5731.40i		−	0.0388685i
$385$	−63765.9	−	27759.7i	−0.430196	−	0.187281i
$386$	22130.0			0.148527
$387$	161785.	−	52567.2i	1.08023	−	0.350988i
$388$	43922.7	+	31911.7i	0.291760	+	0.211976i
$389$	−221746.	+	161108.i	−1.46540	+	1.06468i	−0.483491	+	0.875349i	$0.660631\pi$
$389$	−221746.	+	161108.i	−1.46540	+	1.06468i	−0.981914	+	0.189329i	$0.939369\pi$
$390$	−26844.1	+	82617.7i	−0.176490	+	0.543180i
$391$	94854.8	+	30820.2i	0.620449	+	0.201596i
$392$	29591.2	+	40728.7i	0.192571	+	0.265051i
$393$	3422.00	−	4709.98i	0.0221562	−	0.0304954i
$394$	−1287.65	−	3962.98i	−0.00829479	−	0.0255287i
$395$		−	91529.3i		−	0.586632i
$396$	−13661.6	−	61752.5i	−0.0871187	−	0.393790i
$397$	49313.3			0.312884			0.156442	−	0.987687i	$-0.449998\pi$
$397$	49313.3			0.312884			0.156442	+	0.987687i	$0.449998\pi$
$398$	70199.6	−	22809.2i	0.443168	−	0.143994i
$399$	15415.1	+	11199.7i	0.0968280	+	0.0703496i
$400$	−64763.9	+	47053.7i	−0.404775	+	0.294086i
$401$	2341.63	−	7206.79i	0.0145623	−	0.0448181i	−0.943511	−	0.331340i	$-0.892499\pi$
$401$	2341.63	−	7206.79i	0.0145623	−	0.0448181i	0.958074	+	0.286522i	$0.0924992\pi$
$402$	−31991.9	−	10394.8i	−0.197965	−	0.0643227i
$403$	−94112.6	−	129535.i	−0.579479	−	0.797584i
$404$	−64261.9	+	88448.9i	−0.393723	+	0.541913i
$405$	40152.5	+	123577.i	0.244795	+	0.753402i
$406$			32290.6i			0.195895i
$407$	−24476.8	−	2367.76i	−0.147763	−	0.0142938i
$408$	15809.8			0.0949745
$409$	−13724.0	+	4459.20i	−0.0820417	+	0.0266570i	−0.349750	−	0.936843i	$-0.613734\pi$
$409$	−13724.0	+	4459.20i	−0.0820417	+	0.0266570i	0.267709	+	0.963500i	$0.413734\pi$
$410$	259678.	+	188667.i	1.54478	+	1.12235i
$411$	−58029.9	+	42161.2i	−0.343533	+	0.249591i
$412$	−3040.95	+	9359.09i	−0.0179149	+	0.0551365i
$413$	−62048.8	−	20160.9i	−0.363775	−	0.118198i
$414$	61365.7	+	84462.6i	0.358034	+	0.492792i
$415$	−240765.	+	331385.i	−1.39797	+	1.92414i
$416$	−10022.8	−	30846.9i	−0.0579163	−	0.178248i
$417$		−	40295.4i		−	0.231731i
$418$	−107007.	+	62968.6i	−0.612437	+	0.360389i
$419$	229500.			1.30724			0.653619	−	0.756824i	$-0.273250\pi$
$419$	229500.			1.30724			0.653619	+	0.756824i	$0.273250\pi$
$420$	17307.3	−	5623.50i	0.0981142	−	0.0318792i
$421$	−9854.14	−	7159.45i	−0.0555974	−	0.0403939i	0.559639	−	0.828736i	$-0.310940\pi$
$421$	−9854.14	−	7159.45i	−0.0555974	−	0.0403939i	−0.615237	+	0.788342i	$0.710940\pi$
$422$	165675.	−	120370.i	0.930320	−	0.675917i
$423$	−31217.1	+	96076.4i	−0.174467	+	0.536953i
$424$	31655.0	+	10285.3i	0.176080	+	0.0572119i
$425$	−129796.	−	178649.i	−0.718593	−	0.989058i
$426$	−55911.9	+	76956.1i	−0.308095	+	0.424057i
$427$	6505.56	+	20022.1i	0.0356803	+	0.109813i
$428$			67706.4i			0.369609i
$429$	43516.6	+	73951.1i	0.236451	+	0.401819i
$430$	−318947.			−1.72497
$431$	−40180.7	+	13055.5i	−0.216303	+	0.0702813i	−0.415164	−	0.909747i	$-0.636276\pi$
$431$	−40180.7	+	13055.5i	−0.216303	+	0.0702813i	0.198861	+	0.980028i	$0.436276\pi$
$432$	29987.2	+	21787.0i	0.160682	+	0.116743i
$433$	−53631.9	+	38965.8i	−0.286053	+	0.207830i	−0.721553	−	0.692359i	$-0.756572\pi$
$433$	−53631.9	+	38965.8i	−0.286053	+	0.207830i	0.435500	+	0.900189i	$0.356572\pi$
$434$	−10365.0	+	31900.1i	−0.0550287	+	0.169361i
$435$	−140244.	−	45568.2i	−0.741152	−	0.240815i
$436$	−35966.1	−	49503.1i	−0.189200	−	0.260411i
$437$	120469.	−	165812.i	0.630831	−	0.868264i
$438$	15740.2	+	48443.3i	0.0820467	+	0.252514i
$439$		−	212489.i		−	1.10257i	−0.834316	−	0.551287i	$-0.814137\pi$
$439$		−	212489.i		−	1.10257i	0.834316	−	0.551287i	$-0.185863\pi$
$440$	−11417.6	+	118030.i	−0.0589753	+	0.609661i
$441$	−145366.			−0.747457
$442$	85090.0	−	27647.4i	0.435546	−	0.141517i
$443$	289268.	+	210166.i	1.47399	+	1.07091i	0.979434	+	0.201766i	$0.0646681\pi$
$443$	289268.	+	210166.i	1.47399	+	1.07091i	0.494553	+	0.869148i	$0.335332\pi$
$444$	5205.78	−	3782.22i	0.0264071	−	0.0191859i
$445$	194829.	−	599624.i	0.983863	−	3.02802i
$446$	76101.5	+	24726.9i	0.382581	+	0.124308i
$447$	61764.3	+	85011.3i	0.309117	+	0.425463i
$448$	−3993.75	+	5496.93i	−0.0198987	+	0.0273882i
$449$	11170.1	+	34378.0i	0.0554069	+	0.170525i	0.974930	−	0.222510i	$-0.0714251\pi$
$449$	11170.1	+	34378.0i	0.0554069	+	0.170525i	−0.919523	+	0.393035i	$0.871425\pi$
$450$		−	231151.i		−	1.14149i
$451$	309561.	−	68484.7i	1.52193	−	0.336698i
$452$	72637.3			0.355536
$453$	71473.2	−	23223.0i	0.348295	−	0.113168i
$454$	−164878.	−	119791.i	−0.799926	−	0.581181i
$455$	83315.6	−	60532.3i	0.402442	−	0.292391i
$456$	10039.5	−	30898.5i	0.0482819	−	0.148596i
$457$	23357.6	+	7589.34i	0.111840	+	0.0363389i	0.364402	−	0.931242i	$-0.381273\pi$
$457$	23357.6	+	7589.34i	0.111840	+	0.0363389i	−0.252563	+	0.967581i	$0.581273\pi$
$458$	−14860.0	−	20453.1i	−0.0708416	−	0.0975051i
$459$	−60098.5	+	82718.4i	−0.285258	+	0.392624i
$460$	−60488.8	−	186165.i	−0.285864	−	0.879798i
$461$			41038.8i			0.193105i	0.995328	+	0.0965523i	$0.0307815\pi$
$461$			41038.8i			0.193105i	−0.995328	+	0.0965523i	$0.969218\pi$
$462$	7174.79	−	16481.0i	0.0336144	−	0.0772146i
$463$	−263948.			−1.23128			−0.615640	−	0.788027i	$-0.711103\pi$
$463$	−263948.			−1.23128			−0.615640	+	0.788027i	$0.711103\pi$
$464$	52363.0	−	17013.8i	0.243214	−	0.0790250i
$465$	−123922.	−	90034.5i	−0.573115	−	0.416393i
$466$	−110789.	+	80493.0i	−0.510182	+	0.370669i
$467$	−7002.66	+	21552.0i	−0.0321092	+	0.0988219i	−0.965827	−	0.259189i	$-0.916545\pi$
$467$	−7002.66	+	21552.0i	−0.0321092	+	0.0988219i	0.933718	+	0.358011i	$0.116545\pi$
$468$	89070.1	+	28940.6i	0.406668	+	0.132135i
$469$	23439.8	+	32262.2i	0.106564	+	0.146672i
$470$	111331.	−	153234.i	0.503987	−	0.693678i
$471$	−4165.16	−	12819.0i	−0.0187754	−	0.0577848i
$472$			111242.i			0.499327i
$473$	−208854.	+	235857.i	−0.933515	+	1.05421i
$474$	23656.8			0.105293
$475$	−431571.	+	140226.i	−1.91278	+	0.621500i
$476$	−15163.1	−	11016.6i	−0.0669226	−	0.0486221i
$477$	−77752.3	+	56490.4i	−0.341725	+	0.248278i
$478$	47333.4	−	145677.i	0.207163	−	0.637581i
$479$	63206.4	+	20537.0i	0.275480	+	0.0895089i	0.443499	−	0.896275i	$-0.353737\pi$
$479$	63206.4	+	20537.0i	0.275480	+	0.0895089i	−0.168019	+	0.985784i	$0.553737\pi$
$480$	−18238.3	−	25102.9i	−0.0791595	−	0.108954i
$481$	21403.8	−	29459.9i	0.0925127	−	0.127333i
$482$	−47343.6	−	145709.i	−0.203783	−	0.627179i
$483$			29671.9i			0.127189i
$484$	79805.5	+	85732.5i	0.340676	+	0.365978i
$485$	293926.			1.24955
$486$	−158133.	+	51380.4i	−0.669497	+	0.217533i
$487$	329613.	+	239478.i	1.38978	+	1.00973i	0.995890	+	0.0905764i	$0.0288709\pi$
$487$	329613.	+	239478.i	1.38978	+	1.00973i	0.393890	+	0.919158i	$0.371129\pi$
$488$	29040.4	−	21099.1i	0.121945	−	0.0885980i
$489$	10419.8	−	32068.8i	0.0435754	−	0.134111i
$490$	259212.	+	84223.2i	1.07960	+	0.350784i
$491$	20767.7	+	28584.3i	0.0861442	+	0.118567i	0.849914	−	0.526921i	$-0.176654\pi$
$491$	20767.7	+	28584.3i	0.0861442	+	0.118567i	−0.763770	+	0.645489i	$0.776654\pi$
$492$	−48763.1	+	67116.7i	−0.201447	+	0.277268i
$493$	46931.8	+	144441.i	0.193096	+	0.594288i
$494$		−	183855.i		−	0.753394i
$495$	−256344.	−	226996.i	−1.04619	−	0.926418i
$496$	57191.1			0.232469
$497$	107249.	−	34847.4i	0.434191	−	0.141077i
$498$	−85650.0	−	62228.4i	−0.345357	−	0.250917i
$499$	−24801.7	+	18019.5i	−0.0996046	+	0.0723670i	−0.636473	−	0.771299i	$-0.719607\pi$
$499$	−24801.7	+	18019.5i	−0.0996046	+	0.0723670i	0.536868	+	0.843666i	$0.319607\pi$
$500$	−67006.8	+	206226.i	−0.268027	+	0.824903i
$501$	−49912.0	−	16217.4i	−0.198852	−	0.0646109i
$502$	−23760.3	−	32703.2i	−0.0942854	−	0.129773i
$503$	164396.	−	226272.i	0.649764	−	0.894323i	−0.349325	−	0.937002i	$-0.613589\pi$
$503$	164396.	−	226272.i	0.649764	−	0.894323i	0.999089	+	0.0426785i	$0.0135891\pi$
$504$	−6062.69	−	18659.0i	−0.0238673	−	0.0734561i
$505$			591890.i			2.32091i
$506$	−177277.	−	77175.1i	−0.692389	−	0.301423i
$507$	−14022.7			−0.0545527
$508$	−52406.3	+	17027.8i	−0.203075	+	0.0659830i
$509$	−122810.	−	89227.0i	−0.474024	−	0.344398i	0.324984	−	0.945720i	$-0.394641\pi$
$509$	−122810.	−	89227.0i	−0.474024	−	0.344398i	−0.799007	+	0.601321i	$0.794641\pi$
$510$	69245.4	−	50309.7i	0.266226	−	0.193425i
$511$	18660.0	−	57429.5i	0.0714611	−	0.219935i
$512$	11018.2	+	3580.04i	0.0420312	+	0.0136568i
$513$	123500.	+	169983.i	0.469281	+	0.645909i
$514$	−63978.8	+	88059.3i	−0.242164	+	0.333311i
$515$	16463.2	+	50668.6i	0.0620727	+	0.191040i
$516$		−	82435.2i		−	0.309609i
$517$	−40412.1	−	182669.i	−0.151193	−	0.683414i
$518$	−7628.34			−0.0284296
$519$	83148.4	−	27016.6i	0.308688	−	0.100299i
$520$	−142059.	−	103212.i	−0.525366	−	0.381701i
$521$	1689.60	−	1227.57i	0.00622455	−	0.00452240i	−0.584669	−	0.811272i	$-0.698775\pi$
$521$	1689.60	−	1227.57i	0.00622455	−	0.00452240i	0.590893	+	0.806750i	$0.298775\pi$
$522$	−49127.0	+	151197.i	−0.180293	+	0.554885i
$523$	−290679.	−	94447.4i	−1.06270	−	0.345292i	−0.275060	−	0.961427i	$-0.588698\pi$
$523$	−290679.	−	94447.4i	−1.06270	−	0.345292i	−0.787641	+	0.616135i	$0.788698\pi$
$524$	6917.11	+	9520.58i	0.0251920	+	0.0346737i
$525$	38614.7	−	53148.6i	0.140099	−	0.192829i
$526$	113672.	+	349846.i	0.410848	+	1.26446i
$527$			157759.i			0.568033i
$528$	−30506.2	−	2951.01i	−0.109426	−	0.0105853i
$529$	39322.4			0.140517
$530$	171375.	−	55683.2i	0.610093	−	0.198231i
$531$	−259865.	−	188803.i	−0.921633	−	0.669606i
$532$	−31159.5	+	22638.7i	−0.110095	+	0.0799887i
$533$	−145077.	+	446503.i	−0.510676	+	1.57170i
$534$	154979.	+	50355.8i	0.543489	+	0.176590i
$535$	215454.	+	296547.i	0.752743	+	1.03606i
$536$	39966.6	−	55009.3i	0.139113	−	0.191473i
$537$	−10220.5	−	31455.5i	−0.0354424	−	0.109081i
$538$		−	199825.i		−	0.690375i
$539$	232021.	−	136533.i	0.798637	−	0.469959i
$540$	200671.			0.688171
$541$	−120348.	+	39103.4i	−0.411192	+	0.133604i	−0.507306	−	0.861766i	$-0.669359\pi$
$541$	−120348.	+	39103.4i	−0.411192	+	0.133604i	0.0961142	+	0.995370i	$0.469359\pi$
$542$	−182453.	−	132560.i	−0.621088	−	0.451247i
$543$	−32242.8	+	23425.8i	−0.109354	+	0.0794500i
$544$	−9875.38	+	30393.3i	−0.0333700	+	0.102702i
$545$	−315055.	−	102368.i	−1.06070	−	0.344643i
$546$	15645.2	+	21533.8i	0.0524804	+	0.0722331i
$547$	208238.	−	286615.i	0.695961	−	0.957908i	−0.304025	−	0.952664i	$-0.598331\pi$
$547$	208238.	−	286615.i	0.695961	−	0.957908i	0.999986	−	0.00524442i	$-0.00166936\pi$
$548$	−44804.4	−	137894.i	−0.149197	−	0.459180i
$549$			103649.i			0.343891i
$550$	217105.	+	368943.i	0.717701	+	1.21965i
$551$	312096.			1.02798
$552$	48116.5	−	15634.0i	0.157912	−	0.0513088i
$553$	−22689.0	−	16484.5i	−0.0741932	−	0.0539045i
$554$	−101396.	+	73668.7i	−0.330372	+	0.240029i
$555$	10765.1	−	33131.5i	0.0349487	−	0.107561i
$556$	77465.1	+	25169.9i	0.250586	+	0.0814202i
$557$	18181.9	+	25025.2i	0.0586042	+	0.0806618i	0.837313	−	0.546724i	$-0.184125\pi$
$557$	18181.9	+	25025.2i	0.0586042	+	0.0806618i	−0.778709	+	0.627385i	$0.784125\pi$
$558$	−97066.1	+	133600.i	−0.311745	+	0.429080i
$559$	−144158.	−	443674.i	−0.461335	−	1.41984i
$560$			36784.8i			0.117298i
$561$	8140.23	−	84150.2i	0.0258649	−	0.267380i
$562$	−221383.			−0.700924
$563$	−338262.	+	109908.i	−1.06718	+	0.346747i	−0.789387	−	0.613896i	$-0.789602\pi$
$563$	−338262.	+	109908.i	−1.06718	+	0.346747i	−0.277789	+	0.960642i	$0.589602\pi$
$564$	39604.9	+	28774.6i	0.124506	+	0.0904590i
$565$	318144.	−	231145.i	0.996613	−	0.724082i
$566$	−78486.6	+	241557.i	−0.244998	+	0.754027i
$567$	37864.6	+	12303.0i	0.117779	+	0.0382687i
$568$	−113018.	−	155556.i	−0.350309	−	0.482160i
$569$	257141.	−	353925.i	0.794232	−	1.09317i	−0.199337	−	0.979931i	$-0.563879\pi$
$569$	257141.	−	353925.i	0.794232	−	1.09317i	0.993568	−	0.113235i	$-0.0361213\pi$
$570$	−54352.5	−	167280.i	−0.167290	−	0.514865i
$571$			1830.95i			0.00561570i	0.999996	+	0.00280785i	$0.000893767\pi$
$571$			1830.95i			0.00561570i	−0.999996	+	0.00280785i	$0.999106\pi$
$572$	−169348.	+	37465.1i	−0.517592	+	0.114508i
$573$	−139763.			−0.425679
$574$	93536.5	−	30391.9i	0.283895	−	0.0922430i
$575$	−571689.	−	415356.i	−1.72912	−	1.25628i
$576$	−27063.4	+	19662.7i	−0.0815714	+	0.0592651i
$577$	71653.2	−	220526.i	0.215221	−	0.662381i	−0.783917	−	0.620865i	$-0.786781\pi$
$577$	71653.2	−	220526.i	0.215221	−	0.662381i	0.999138	−	0.0415155i	$-0.0132186\pi$
$578$	140832.	+	45759.2i	0.421548	+	0.136969i
$579$	18201.2	+	25051.8i	0.0542930	+	0.0747278i
$580$	175203.	−	241147.i	0.520818	−	0.716845i
$581$	38784.1	+	119365.i	0.114895	+	0.353611i
$582$			75968.3i			0.224278i
$583$	71043.8	−	163193.i	0.209021	−	0.480135i
$584$	−102961.			−0.301888
$585$	482212.	−	156680.i	1.40905	−	0.457828i
$586$	−46945.2	−	34107.7i	−0.136709	−	0.0993247i
$587$	−41941.6	+	30472.3i	−0.121722	+	0.0884361i	−0.646981	−	0.762506i	$-0.723969\pi$
$587$	−41941.6	+	30472.3i	−0.121722	+	0.0884361i	0.525259	+	0.850943i	$0.323969\pi$
$588$	−21768.4	+	66996.3i	−0.0629610	+	0.193774i
$589$	308323.	+	100180.i	0.888740	+	0.288769i
$590$	353992.	+	487229.i	1.01693	+	1.39968i
$591$	3427.16	−	4717.09i	0.00981205	−	0.0135051i
$592$	4019.34	+	12370.3i	0.0114686	+	0.0352968i
$593$		−	94653.9i		−	0.269171i	−0.990902	−	0.134586i	$-0.957030\pi$
$593$		−	94653.9i		−	0.269171i	0.990902	−	0.134586i	$-0.0429704\pi$
$594$	131404.	−	148394.i	0.372423	−	0.420574i
$595$	−101469.			−0.286616
$596$	−202008.	+	65636.5i	−0.568692	+	0.184779i
$597$	83557.7	+	60708.2i	0.234443	+	0.170333i
$598$	231627.	−	168287.i	0.647720	−	0.470596i
$599$	35391.5	−	108924.i	0.0986382	−	0.303577i	−0.889547	−	0.456844i	$-0.848980\pi$
$599$	35391.5	−	108924.i	0.0986382	−	0.303577i	0.988185	+	0.153267i	$0.0489796\pi$
$600$	−106533.	−	34614.6i	−0.295924	−	0.0961515i
$601$	−190529.	−	262240.i	−0.527486	−	0.726023i	0.459258	−	0.888303i	$-0.348115\pi$
$601$	−190529.	−	262240.i	−0.527486	−	0.726023i	−0.986745	+	0.162280i	$0.948115\pi$
$602$	−57442.5	+	79062.8i	−0.158504	+	0.218162i
$603$	60671.0	+	186726.i	0.166858	+	0.513535i
$604$			151908.i			0.416397i
$605$	622355.	+	121544.i	1.70031	+	0.332064i
$606$	−152980.			−0.416572
$607$	−666226.	+	216470.i	−1.80819	+	0.587517i	−0.999999	−	0.00140328i	$-0.999553\pi$
$607$	−666226.	+	216470.i	−1.80819	+	0.587517i	−0.808191	+	0.588920i	$0.799553\pi$
$608$	53129.2	+	38600.6i	0.143723	+	0.104421i
$609$	−36553.9	+	26558.0i	−0.0985597	+	0.0716078i
$610$	60052.8	−	184823.i	0.161389	−	0.496704i
$611$	263477.	+	85608.7i	0.705764	+	0.229317i
$612$	−54238.8	−	74653.4i	−0.144813	−	0.199318i
$613$	−351341.	+	483580.i	−0.934992	+	1.28691i	0.0228878	+	0.999738i	$0.492714\pi$
$613$	−351341.	+	483580.i	−0.934992	+	1.28691i	−0.957880	+	0.287168i	$0.907286\pi$
$614$	−116967.	−	359988.i	−0.310261	−	0.954886i
$615$			449137.i			1.18749i
$616$	27201.9	+	24087.6i	0.0716866	+	0.0634794i
$617$	−704195.			−1.84979			−0.924896	−	0.380221i	$-0.875848\pi$
$617$	−704195.			−1.84979			−0.924896	+	0.380221i	$0.875848\pi$
$618$	−13095.9	+	4255.11i	−0.0342892	+	0.0111412i
$619$	−31537.5	−	22913.3i	−0.0823087	−	0.0598008i	0.545870	−	0.837870i	$-0.316199\pi$
$619$	−31537.5	−	22913.3i	−0.0823087	−	0.0598008i	−0.628179	+	0.778069i	$0.716199\pi$
$620$	250491.	−	181992.i	0.651641	−	0.473445i
$621$	−101108.	+	311180.i	−0.262183	+	0.806915i
$622$	113740.	+	36956.5i	0.293991	+	0.0955235i
$623$	−113550.	−	156288.i	−0.292558	−	0.402671i
$624$	26676.3	−	36716.7i	0.0685103	−	0.0942963i
$625$	121186.	+	372973.i	0.310237	+	0.954811i
$626$			488716.i			1.24712i
$627$	−159293.	−	69346.1i	−0.405192	−	0.176395i
$628$	27245.4			0.0690834
$629$	−34122.9	+	11087.2i	−0.0862471	+	0.0280234i
$630$	−85930.3	−	62432.0i	−0.216504	−	0.157299i
$631$	15476.7	−	11244.5i	0.0388706	−	0.0282411i	−0.568180	−	0.822904i	$-0.692352\pi$
$631$	15476.7	−	11244.5i	0.0388706	−	0.0282411i	0.607051	+	0.794663i	$0.292352\pi$
$632$	−14776.8	+	45478.4i	−0.0369954	+	0.113860i
$633$	272525.	+	88548.8i	0.680141	+	0.220991i
$634$	−140201.	−	192970.i	−0.348797	−	0.480078i
$635$	−175348.	+	241346.i	−0.434864	+	0.598540i
$636$	14391.9	+	44293.8i	0.0355799	+	0.109504i
$637$			398647.i			0.982449i
$638$	−63597.4	−	287470.i	−0.156242	−	0.706238i
$639$	555201.			1.35972
$640$	59650.9	−	19381.8i	0.145632	−	0.0473187i
$641$	277946.	+	201939.i	0.676462	+	0.491479i	0.872182	−	0.489181i	$-0.162704\pi$
$641$	277946.	+	201939.i	0.676462	+	0.491479i	−0.195720	+	0.980660i	$0.562704\pi$
$642$	−76645.8	+	55686.4i	−0.185959	+	0.135107i
$643$	−22016.3	+	67759.1i	−0.0532503	+	0.163887i	−0.974145	−	0.225924i	$-0.927460\pi$
$643$	−22016.3	+	67759.1i	−0.0532503	+	0.163887i	0.920895	+	0.389812i	$0.127460\pi$
$644$	−57042.1	−	18534.1i	−0.137538	−	0.0446889i
$645$	−262324.	−	361058.i	−0.630548	−	0.867875i
$646$	−106478.	+	146555.i	−0.255150	+	0.351184i
$647$	42270.7	+	130096.i	0.100979	+	0.310781i	0.988766	−	0.149474i	$-0.0477579\pi$
$647$	42270.7	+	130096.i	0.100979	+	0.310781i	−0.887787	+	0.460255i	$0.847758\pi$
$648$		−	67884.4i		−	0.161666i
$649$	592103.	+	57276.8i	1.40575	+	0.135984i
$650$	−633900.			−1.50036
$651$	−44636.8	+	14503.4i	−0.105325	+	0.0342222i
$652$	55141.5	+	40062.6i	0.129713	+	0.0942419i
$653$	−439262.	+	319143.i	−1.03014	+	0.748443i	−0.968337	−	0.249646i	$-0.919686\pi$
$653$	−439262.	+	319143.i	−1.03014	+	0.748443i	−0.0618056	+	0.998088i	$0.519686\pi$
$654$	26458.0	−	81429.5i	0.0618589	−	0.190382i
$655$	60592.4	+	19687.7i	0.141233	+	0.0458893i
$656$	−98568.0	−	135667.i	−0.229049	−	0.315259i
$657$	174747.	−	240519.i	0.404836	−	0.557209i
$658$	−17933.9	−	55194.9i	−0.0414213	−	0.127482i
$659$		−	702060.i		−	1.61660i	−0.588768	−	0.808302i	$-0.700387\pi$
$659$		−	702060.i		−	1.61660i	0.588768	−	0.808302i	$-0.299613\pi$
$660$	−143005.	+	84151.2i	−0.328294	+	0.193185i
$661$	−226372.			−0.518108			−0.259054	−	0.965863i	$-0.583411\pi$
$661$	−226372.			−0.518108			−0.259054	+	0.965863i	$0.583411\pi$
$662$	349879.	−	113683.i	0.798367	−	0.259405i
$663$	101282.	+	73585.4i	0.230411	+	0.167403i
$664$	173130.	−	125786.i	0.392677	−	0.285296i
$665$	−64434.9	+	198310.i	−0.145706	+	0.448438i
$666$	−35719.0	−	11605.8i	−0.0805287	−	0.0261654i
$667$	285669.	+	393190.i	0.642113	+	0.883793i
$668$	62353.6	−	85822.4i	0.139736	−	0.192330i
$669$	34599.5	+	106486.i	0.0773069	+	0.237926i
$670$		−	368116.i		−	0.820039i
$671$	−97350.6	−	165435.i	−0.216219	−	0.367437i
$672$	−9507.44			−0.0210535
$673$	−41554.0	+	13501.7i	−0.0917450	+	0.0298097i	−0.354530	−	0.935045i	$-0.615359\pi$
$673$	−41554.0	+	13501.7i	−0.0917450	+	0.0298097i	0.262785	+	0.964854i	$0.415359\pi$
$674$	187194.	+	136005.i	0.412072	+	0.299388i
$675$	586073.	−	425807.i	1.28630	−	0.934555i
$676$	8759.08	−	26957.7i	0.0191675	−	0.0589914i
$677$	−488471.	−	158714.i	−1.06577	−	0.346288i	−0.276929	−	0.960891i	$-0.589317\pi$
$677$	−488471.	−	158714.i	−1.06577	−	0.346288i	−0.788837	+	0.614602i	$0.789317\pi$
$678$	59741.9	+	82227.7i	0.129963	+	0.178879i
$679$	52936.2	−	72860.5i	0.114819	−	0.158035i
$680$	53463.8	+	164545.i	0.115622	+	0.355849i
$681$		−	285171.i		−	0.614909i
$682$	29446.8	−	304408.i	0.0633096	−	0.654467i
$683$	−289751.			−0.621131			−0.310566	−	0.950552i	$-0.600518\pi$
$683$	−289751.			−0.621131			−0.310566	+	0.950552i	$0.600518\pi$
$684$	−180344.	+	58597.4i	−0.385469	+	0.125247i
$685$	−635041.	−	461384.i	−1.35338	−	0.983290i
$686$	140472.	−	102059.i	0.298499	−	0.216872i
$687$	10931.6	−	33644.0i	0.0231617	−	0.0712844i
$688$	158476.	+	51492.0i	0.334801	+	0.108783i
$689$	154917.	+	213225.i	0.326333	+	0.449159i
$690$	160995.	−	221590.i	0.338153	−	0.465428i
$691$	−148192.	−	456087.i	−0.310361	−	0.955194i	−0.977622	−	0.210370i	$-0.932533\pi$
$691$	−148192.	−	456087.i	−0.310361	−	0.955194i	0.667261	−	0.744824i	$-0.267467\pi$
$692$			176723.i			0.369045i
$693$	−102437.	+	22662.3i	−0.213300	+	0.0471887i
$694$	653568.			1.35697
$695$	419384.	−	136266.i	0.868245	−	0.282110i
$696$	62327.0	+	45283.2i	0.128664	+	0.0934800i
$697$	374232.	−	271896.i	0.770328	−	0.559676i
$698$	11308.0	−	34802.4i	0.0232100	−	0.0714330i
$699$	−182241.	−	59213.7i	−0.372986	−	0.121190i
$700$	78054.3	+	107433.i	0.159294	+	0.219250i
$701$	397842.	−	547582.i	0.809607	−	1.11433i	−0.181777	−	0.983340i	$-0.558185\pi$
$701$	397842.	−	547582.i	0.809607	−	1.11433i	0.991384	−	0.130989i	$-0.0418152\pi$
$702$	90699.7	+	279145.i	0.184048	+	0.566442i
$703$			73729.8i			0.149188i
$704$	24728.4	−	56802.8i	0.0498942	−	0.114610i
$705$	265031.			0.533235
$706$	−158971.	+	51653.0i	−0.318941	+	0.103630i
$707$	146722.	+	106600.i	0.293533	+	0.213264i
$708$	−125930.	+	91493.2i	−0.251224	+	0.182525i
$709$	−69762.5	+	214707.i	−0.138781	+	0.427124i	−0.996159	−	0.0875635i	$-0.972092\pi$
$709$	−69762.5	+	214707.i	−0.138781	+	0.427124i	0.857378	+	0.514687i	$0.172092\pi$
$710$	−990016.	−	321676.i	−1.96393	−	0.638119i
$711$	−81159.3	−	111706.i	−0.160546	−	0.220972i
$712$	−193611.	+	266483.i	−0.381918	+	0.525665i
$713$	156005.	+	480133.i	0.306873	+	0.944457i
$714$		−	26225.9i		−	0.0514439i
$715$	−622505.	+	702988.i	−1.21767	+	1.37511i
$716$	66855.0			0.130409
$717$	203841.	−	66232.0i	0.396510	−	0.128834i
$718$	127801.	+	92853.1i	0.247906	+	0.180114i
$719$	−752504.	+	546726.i	−1.45563	+	1.05758i	−0.471155	+	0.882050i	$0.656163\pi$
$719$	−752504.	+	546726.i	−1.45563	+	1.05758i	−0.984475	+	0.175527i	$0.943837\pi$
$720$	−55964.6	+	172241.i	−0.107956	+	0.332256i
$721$	15525.2	+	5044.43i	0.0298652	+	0.00970379i
$722$	2149.07	+	2957.93i	0.00412264	+	0.00567432i
$723$	126008.	−	173435.i	0.241058	−	0.331788i
$724$	−24894.4	−	76617.0i	−0.0474924	−	0.146167i
$725$		−	1.07605e6i		−	2.04719i
$726$	−31414.3	+	160855.i	−0.0596012	+	0.305183i
$727$	141940.			0.268556			0.134278	−	0.990944i	$-0.457128\pi$
$727$	141940.			0.268556			0.134278	+	0.990944i	$0.457128\pi$
$728$	−51169.9	+	16626.1i	−0.0965498	+	0.0313709i
$729$	8373.95	+	6084.03i	0.0157571	+	0.0114482i
$730$	−450957.	+	327639.i	−0.846231	+	0.614823i
$731$	−142039.	+	437150.i	−0.265810	+	0.818079i
$732$	47769.6	+	15521.3i	0.0891517	+	0.0289672i
$733$	−599214.	−	824747.i	−1.11525	−	1.53502i	−0.813441	−	0.581648i	$-0.802408\pi$
$733$	−599214.	−	824747.i	−1.11525	−	1.53502i	−0.301813	−	0.953367i	$-0.597592\pi$
$734$	−263163.	+	362213.i	−0.488465	+	0.672314i
$735$	117851.	+	362707.i	0.218151	+	0.671401i
$736$			102266.i			0.188789i
$737$	−272217.	−	241052.i	−0.501165	−	0.443787i
$738$	484214.			0.889047
$739$	902735.	−	293316.i	1.65299	−	0.537091i	0.673609	−	0.739088i	$-0.264743\pi$
$739$	902735.	−	293316.i	1.65299	−	0.537091i	0.979386	+	0.201997i	$0.0647432\pi$
$740$	56968.7	+	41390.2i	0.104033	+	0.0755847i
$741$	208130.	−	151215.i	0.379051	−	0.275397i
$742$	17061.6	−	52510.3i	0.0309894	−	0.0953755i
$743$	432128.	+	140407.i	0.782771	+	0.254338i	0.673023	−	0.739622i	$-0.264996\pi$
$743$	432128.	+	140407.i	0.782771	+	0.254338i	0.109748	+	0.993959i	$0.464996\pi$
$744$	47037.9	+	64742.1i	0.0849771	+	0.116961i
$745$	−675908.	+	930308.i	−1.21780	+	1.67615i
$746$	116897.	+	359771.i	0.210051	+	0.646471i
$747$			617923.i			1.10737i
$748$	156688.	+	68212.2i	0.280048	+	0.121916i
$749$	112314.			0.200202
$750$	−288565.	+	93760.5i	−0.513005	+	0.166685i
$751$	337489.	+	245200.i	0.598383	+	0.434751i	0.845305	−	0.534285i	$-0.179419\pi$
$751$	337489.	+	245200.i	0.598383	+	0.434751i	−0.246921	+	0.969036i	$0.579419\pi$
$752$	−80055.8	+	58164.0i	−0.141565	+	0.102853i
$753$	17479.0	−	53794.8i	0.0308266	−	0.0948747i
$754$	414638.	+	134724.i	0.729335	+	0.236975i
$755$	483399.	+	665341.i	0.848031	+	1.16721i
$756$	36140.9	−	49743.7i	0.0632348	−	0.0870352i
$757$	−344073.	−	1.05895e6i	−0.600425	−	1.84792i	−0.525620	−	0.850719i	$-0.676167\pi$
$757$	−344073.	−	1.05895e6i	−0.600425	−	1.84792i	−0.0748048	−	0.997198i	$-0.523833\pi$
$758$		−	152445.i		−	0.265322i
$759$	−58439.8	−	264157.i	−0.101444	−	0.458541i
$760$	355534.			0.615537
$761$	230550.	−	74910.2i	0.398103	−	0.129352i	−0.103121	−	0.994669i	$-0.532883\pi$
$761$	230550.	−	74910.2i	0.398103	−	0.129352i	0.501225	+	0.865317i	$0.332883\pi$
$762$	−62378.6	−	45320.7i	−0.107430	−	0.0780524i
$763$	−82117.3	+	59661.7i	−0.141054	+	0.102482i
$764$	87300.7	−	268684.i	0.149565	−	0.460315i
$765$	−475121.	−	154376.i	−0.811860	−	0.263789i
$766$	−81194.3	−	111754.i	−0.138378	−	0.190461i
$767$	−517766.	+	712643.i	−0.880121	+	1.21138i
$768$	5009.43	+	15417.4i	0.00849309	+	0.0261390i
$769$			502205.i			0.849235i	0.905373	+	0.424618i	$0.139591\pi$
$769$			502205.i			0.849235i	−0.905373	+	0.424618i	$0.860409\pi$
$770$	195793.	+	18939.9i	0.330229	+	0.0319445i
$771$	−152306.			−0.256218
$772$	−59529.5	+	19342.3i	−0.0998844	+	0.0324544i
$773$	514266.	+	373636.i	0.860654	+	0.625302i	0.928063	−	0.372423i	$-0.121473\pi$
$773$	514266.	+	373636.i	0.860654	+	0.625302i	−0.0674085	+	0.997725i	$0.521473\pi$
$774$	−389256.	+	282811.i	−0.649760	+	0.472078i
$775$	345403.	−	1.06304e6i	0.575073	−	1.76989i
$776$	−146044.	−	47452.5i	−0.242527	−	0.0788017i
$777$	−6274.08	−	8635.52i	−0.0103922	−	0.0143036i
$778$	455683.	−	627194.i	0.752841	−	1.03620i
$779$	−293745.	−	904053.i	−0.484055	−	1.48977i
$780$		−	245704.i		−	0.403853i
$781$	−886163.	+	521463.i	−1.45282	+	0.854912i
$782$	−282097.			−0.461301
$783$	−473852.	+	153964.i	−0.772892	+	0.251128i
$784$	−115198.	−	83696.5i	−0.187419	−	0.136168i
$785$	119332.	−	86699.7i	0.193650	−	0.140695i
$786$	−5088.49	+	15660.8i	−0.00823652	+	0.0253494i
$787$	573732.	+	186417.i	0.926317	+	0.300979i	0.733056	−	0.680168i	$-0.238093\pi$
$787$	573732.	+	186417.i	0.926317	+	0.300979i	0.193262	+	0.981147i	$0.438093\pi$
$788$	6927.54	+	9534.94i	0.0111565	+	0.0153556i
$789$	−302545.	+	416417.i	−0.485999	+	0.668921i
$790$	79999.5	+	246213.i	0.128184	+	0.394509i
$791$		−	120493.i		−	0.192579i
$792$	90723.3	+	154173.i	0.144633	+	0.245787i
$793$	284243.			0.452006
$794$	−132652.	+	43101.4i	−0.210414	+	0.0683676i
$795$	203986.	+	148204.i	0.322750	+	0.234491i
$796$	−168900.	+	122713.i	−0.266566	+	0.193671i
$797$	268673.	−	826889.i	0.422967	−	1.30176i	−0.481960	−	0.876193i	$-0.660075\pi$
$797$	268673.	−	826889.i	0.422967	−	1.30176i	0.904927	−	0.425566i	$-0.139925\pi$
$798$	−51255.5	−	16653.9i	−0.0804886	−	0.0261523i
$799$	−160443.	−	220831.i	−0.251320	−	0.345912i
$800$	133088.	−	183180.i	0.207950	−	0.286219i
$801$	−293910.	−	904561.i	−0.458088	−	1.40985i
$802$			21432.9i			0.0333221i
$803$	−53012.8	+	548023.i	−0.0822147	+	0.849900i
$804$	95143.5			0.147186
$805$	−308817.	+	100341.i	−0.476551	+	0.154841i
$806$	366380.	+	266191.i	0.563977	+	0.409753i
$807$	226208.	−	164350.i	0.347345	−	0.252361i
$808$	95557.0	−	294094.i	0.146366	−	0.450468i
$809$	344281.	+	111864.i	0.526036	+	0.170920i	0.559983	−	0.828504i	$-0.310808\pi$
$809$	344281.	+	111864.i	0.526036	+	0.170920i	−0.0339467	+	0.999424i	$0.510808\pi$
$810$	−216020.	−	297326.i	−0.329249	−	0.453172i
$811$	332769.	−	458018.i	0.505943	−	0.696371i	−0.477285	−	0.878748i	$-0.658379\pi$
$811$	332769.	−	458018.i	0.505943	−	0.696371i	0.983229	+	0.182377i	$0.0583792\pi$
$812$	−28223.0	−	86861.4i	−0.0428046	−	0.131739i
$813$		−	315570.i		−	0.477435i
$814$	67912.1	−	15024.3i	0.102494	−	0.0226749i
$815$	369000.			0.555535
$816$	−42528.4	+	13818.3i	−0.0638702	+	0.0207527i
$817$	764162.	+	555196.i	1.14483	+	0.831768i
$818$	33020.0	−	23990.4i	0.0493481	−	0.0358535i
$819$	48007.7	−	147752.i	0.0715719	−	0.220276i
$820$	−863434.	−	280547.i	−1.28411	−	0.417232i
$821$	426408.	+	586901.i	0.632615	+	0.870720i	0.998195	−	0.0600604i	$-0.0191293\pi$
$821$	426408.	+	586901.i	0.632615	+	0.870720i	−0.365580	+	0.930780i	$0.619129\pi$
$822$	119250.	−	164133.i	0.176488	−	0.242914i
$823$	291256.	+	896394.i	0.430007	+	1.32343i	0.898118	+	0.439756i	$0.144935\pi$
$823$	291256.	+	896394.i	0.430007	+	1.32343i	−0.468110	+	0.883670i	$0.655065\pi$
$824$		−	27833.8i		−	0.0409938i
$825$	−239093.	+	549213.i	−0.351285	+	0.806925i
$826$	184532.			0.270465
$827$	303169.	−	98505.6i	0.443276	−	0.144029i	−0.0788708	−	0.996885i	$-0.525131\pi$
$827$	303169.	−	98505.6i	0.443276	−	0.144029i	0.522146	+	0.852856i	$0.325131\pi$
$828$	−238896.	−	173568.i	−0.348457	−	0.253169i
$829$	−793128.	+	576241.i	−1.15408	+	0.838485i	−0.989017	−	0.147799i	$-0.952781\pi$
$829$	−793128.	+	576241.i	−1.15408	+	0.838485i	−0.165058	+	0.986284i	$0.552781\pi$
$830$	358016.	−	1.10186e6i	0.519692	−	1.59945i
$831$	−166791.	−	54193.6i	−0.241529	−	0.0784776i
$832$	53922.4	+	74217.8i	0.0778973	+	0.107216i
$833$	230873.	−	317770.i	0.332724	−	0.457955i
$834$	35219.5	+	108394.i	0.0506350	+	0.155838i
$835$		−	574313.i		−	0.823713i
$836$	232813.	−	262913.i	0.333115	−	0.376184i
$837$	−517543.			−0.738747
$838$	−617354.	+	200590.i	−0.879116	+	0.285642i
$839$	−423441.	−	307648.i	−0.601546	−	0.437048i	0.244882	−	0.969553i	$-0.421251\pi$
$839$	−423441.	−	307648.i	−0.601546	−	0.437048i	−0.846427	+	0.532505i	$0.821251\pi$
$840$	−41641.5	+	30254.4i	−0.0590158	+	0.0428775i
$841$	−10133.9	+	31188.9i	−0.0143280	+	0.0440969i
$842$	32765.2	+	10646.1i	0.0462156	+	0.0150163i
$843$	−182080.	−	250612.i	−0.256217	−	0.352652i
$844$	−340458.	+	468600.i	−0.477945	+	0.657835i
$845$	−47420.3	−	145945.i	−0.0664127	−	0.204397i
$846$		−	285730.i		−	0.399222i
$847$	142216.	−	132384.i	0.198235	−	0.184531i
$848$	−94141.4			−0.130915
$849$	−338003.	+	109824.i	−0.468927	+	0.152364i
$850$	505295.	+	367118.i	0.699370	+	0.508122i
$851$	−92887.4	+	67486.7i	−0.128262	+	0.0931877i
$852$	83140.6	−	255880.i	0.114534	−	0.352499i
$853$	328116.	+	106611.i	0.450951	+	0.146523i	0.525683	−	0.850681i	$-0.323810\pi$
$853$	328116.	+	106611.i	0.450951	+	0.146523i	−0.0747314	+	0.997204i	$0.523810\pi$
$854$	−34999.8	−	48173.2i	−0.0479900	−	0.0660525i
$855$	−603421.	+	830537.i	−0.825445	+	1.13613i
$856$	−59177.6	−	182130.i	−0.0807625	−	0.248561i
$857$		−	652071.i		−	0.887837i	−0.896067	−	0.443919i	$-0.853588\pi$
$857$		−	652071.i		−	0.887837i	0.896067	−	0.443919i	$-0.146412\pi$
$858$	−181695.	−	160893.i	−0.246813	−	0.218556i
$859$	−559418.			−0.758142			−0.379071	−	0.925368i	$-0.623756\pi$
$859$	−559418.			−0.758142			−0.379071	+	0.925368i	$0.623756\pi$
$860$	857964.	−	278770.i	1.16004	−	0.376919i
$861$	111335.	+	80889.9i	0.150185	+	0.109116i
$862$	96675.0	−	70238.5i	0.130107	−	0.0945281i
$863$	−116919.	+	359840.i	−0.156987	+	0.483157i	−0.998357	−	0.0573033i	$-0.981750\pi$
$863$	−116919.	+	359840.i	−0.156987	+	0.483157i	0.841370	+	0.540460i	$0.181750\pi$
$864$	−99707.9	−	32397.1i	−0.133568	−	0.0433988i
$865$	562363.	+	774026.i	0.751596	+	1.03448i
$866$	110212.	−	151694.i	0.146958	−	0.202270i
$867$	64029.4	+	197062.i	0.0851806	+	0.262159i
$868$		−	94870.5i		−	0.125919i
$869$	234457.	+	102068.i	0.310474	+	0.135161i
$870$	417085.			0.551044
$871$	512071.	−	166382.i	0.674985	−	0.219316i
$872$	140016.	+	101727.i	0.184138	+	0.133784i
$873$	358719.	−	260625.i	0.470680	−	0.341969i
$874$	−179137.	+	551326.i	−0.234510	+	0.721748i
$875$	342094.	+	111153.i	0.446817	+	0.145180i
$876$	−84681.9	−	116555.i	−0.110353	−	0.151887i
$877$	133607.	−	183894.i	0.173712	−	0.239094i	−0.713280	−	0.700880i	$-0.752791\pi$
$877$	133607.	−	183894.i	0.173712	−	0.239094i	0.886992	+	0.461785i	$0.152791\pi$
$878$	185722.	+	571594.i	0.240921	+	0.741479i
$879$		−	81196.0i		−	0.105089i
$880$	−72449.0	−	327480.i	−0.0935550	−	0.422883i
$881$	721351.			0.929383			0.464692	−	0.885473i	$-0.346165\pi$
$881$	721351.			0.929383			0.464692	+	0.885473i	$0.346165\pi$
$882$	391034.	−	127055.i	0.502664	−	0.163325i
$883$	−173179.	−	125822.i	−0.222113	−	0.161374i	0.471165	−	0.882045i	$-0.343834\pi$
$883$	−173179.	−	125822.i	−0.222113	−	0.161374i	−0.693277	+	0.720671i	$0.743834\pi$
$884$	−204727.	+	148743.i	−0.261981	+	0.190340i
$885$	−260410.	+	801461.i	−0.332485	+	1.02328i
$886$	−961822.	−	312515.i	−1.22526	−	0.398110i
$887$	−720290.	−	991394.i	−0.915504	−	1.26008i	−0.965252	−	0.261322i	$-0.915842\pi$
$887$	−720290.	−	991394.i	−0.915504	−	1.26008i	0.0497477	−	0.998762i	$-0.484158\pi$
$888$	−10697.7	+	14724.2i	−0.0135664	+	0.0186726i
$889$	28246.3	+	86933.2i	0.0357403	+	0.109997i
$890$			1.78327e6i			2.25132i
$891$	−361325.	−	34952.6i	−0.455137	−	0.0440275i
$892$	−226325.			−0.284448
$893$	−533473.	+	173336.i	−0.668974	+	0.217363i
$894$	−240448.	−	174696.i	−0.300848	−	0.218579i
$895$	292818.	−	212745.i	0.365554	−	0.265591i
$896$	5938.68	−	18277.4i	0.00739731	−	0.0227666i
$897$	381012.	+	123798.i	0.473537	+	0.153862i
$898$	−60094.9	−	82713.6i	−0.0745221	−	0.102571i
$899$	−451861.	+	621934.i	−0.559095	+	0.769528i
$900$	202033.	+	621795.i	0.249424	+	0.767648i
$901$		−	259685.i		−	0.319888i
$902$	−772860.	+	454790.i	−0.949922	+	0.558982i
$903$	−136746.			−0.167703
$904$	−195394.	+	63487.4i	−0.239097	+	0.0776874i
$905$	−352844.	−	256356.i	−0.430810	−	0.313001i
$906$	−171965.	+	124940.i	−0.209500	+	0.152210i
$907$	−313569.	+	965067.i	−0.381170	+	1.17312i	0.558050	+	0.829807i	$0.311550\pi$
$907$	−313569.	+	965067.i	−0.381170	+	1.17312i	−0.939221	+	0.343314i	$0.888450\pi$
$908$	548221.	+	178128.i	0.664942	+	0.216053i
$909$	524830.	+	722367.i	0.635172	+	0.874239i
$910$	−171211.	+	235652.i	−0.206752	+	0.284570i
$911$	369150.	+	1.13613e6i	0.444802	+	1.36896i	0.882701	+	0.469935i	$0.155723\pi$
$911$	369150.	+	1.13613e6i	0.444802	+	1.36896i	−0.437899	+	0.899024i	$0.644277\pi$
$912$			91891.7i			0.110481i
$913$	−580373.	−	986274.i	−0.696251	−	1.18319i
$914$	−69465.1			−0.0831523
$915$	258617.	−	84029.9i	0.308898	−	0.100367i
$916$	57850.0	+	42030.5i	0.0689465	+	0.0500926i
$917$	15793.0	−	11474.3i	0.0187814	−	0.0136455i
$918$	89366.0	−	275040.i	0.106044	−	0.326370i
$919$	−1.42102e6	−	461717.i	−1.68255	−	0.546695i	−0.697150	−	0.716925i	$-0.745549\pi$
$919$	−1.42102e6	−	461717.i	−1.68255	−	0.546695i	−0.985404	+	0.170230i	$0.945549\pi$
$920$	325429.	+	447914.i	0.384486	+	0.529199i
$921$	311316.	−	428490.i	0.367014	−	0.505151i
$922$	−35869.2	−	110394.i	−0.0421949	−	0.129863i
$923$		−	1.52256e6i		−	1.78719i
$924$	−4895.23	+	50604.7i	−0.00573362	+	0.0592717i
$925$	254207.			0.297101
$926$	710020.	−	230699.i	0.828034	−	0.269045i
$927$	65020.5	+	47240.1i	0.0756642	+	0.0549733i
$928$	−125985.	+	91533.8i	−0.146293	+	0.106288i
$929$	−147042.	+	452547.i	−0.170376	+	0.524364i	−0.999392	−	0.0348610i	$-0.988901\pi$
$929$	−147042.	+	452547.i	−0.170376	+	0.524364i	0.829016	+	0.559225i	$0.188901\pi$
$930$	412042.	+	133881.i	0.476404	+	0.154793i
$931$	−474436.	−	653005.i	−0.547367	−	0.753385i
$932$	227669.	−	313359.i	0.262103	−	0.360753i
$933$	51712.0	+	159153.i	0.0594057	+	0.182832i
$934$		−	64095.2i		−	0.0734737i
$935$	903341.	−	199848.i	1.03330	−	0.228600i
$936$	−264893.			−0.302356
$937$	869952.	−	282665.i	0.990869	−	0.321953i	0.231658	−	0.972797i	$-0.425585\pi$
$937$	869952.	−	282665.i	0.990869	−	0.321953i	0.759211	+	0.650845i	$0.225585\pi$
$938$	−91251.2	−	66297.9i	−0.103713	−	0.0753519i
$939$	−553241.	+	401953.i	−0.627456	+	0.455874i
$940$	−165548.	+	509504.i	−0.187356	+	0.576623i
$941$	790180.	+	256745.i	0.892374	+	0.289950i	0.719086	−	0.694921i	$-0.244561\pi$
$941$	790180.	+	256745.i	0.892374	+	0.289950i	0.173288	+	0.984871i	$0.444561\pi$
$942$	22408.5	+	30842.6i	0.0252529	+	0.0347576i
$943$	870087.	−	1.19757e6i	0.978451	−	1.34672i
$944$	−97229.2	−	299241.i	−0.109107	−	0.335797i
$945$		−	332879.i		−	0.372755i
$946$	355670.	−	817000.i	0.397434	−	0.912935i
$947$	−322279.			−0.359362			−0.179681	−	0.983725i	$-0.557506\pi$
$947$	−322279.			−0.359362			−0.179681	+	0.983725i	$0.557506\pi$
$948$	−63636.5	+	20676.8i	−0.0708092	+	0.0230073i
$949$	−659590.	−	479220.i	−0.732389	−	0.532112i
$950$	1.03836e6	−	754414.i	1.15054	−	0.835916i
$951$	103137.	−	317424.i	0.114039	−	0.350977i
$952$	50417.4	+	16381.6i	0.0556297	+	0.0180752i
$953$	−182953.	−	251813.i	−0.201444	−	0.277263i	0.696329	−	0.717723i	$-0.254816\pi$
$953$	−182953.	−	251813.i	−0.201444	−	0.277263i	−0.897772	+	0.440459i	$0.854816\pi$
$954$	159779.	−	219917.i	0.175559	−	0.241636i
$955$	−472632.	−	1.45461e6i	−0.518223	−	1.59493i
$956$			433241.i			0.474039i
$957$	273118.	−	308429.i	0.298213	−	0.336769i
$958$	−187975.			−0.204818
$959$	−228743.	+	74323.0i	−0.248720	+	0.0808139i
$960$	71001.8	+	51585.8i	0.0770419	+	0.0559742i
$961$	101111.	−	73461.5i	0.109484	−	0.0795450i
$962$	−31827.3	+	97954.5i	−0.0343914	+	0.105846i
$963$	525898.	+	170875.i	0.567086	+	0.184257i
$964$	254708.	+	350576.i	0.274087	+	0.377248i
$965$	−199182.	+	274151.i	−0.213893	+	0.294398i
$966$	−25934.2	−	79817.2i	−0.0277919	−	0.0855346i
$967$			852868.i			0.912072i	0.889961	+	0.456036i	$0.150731\pi$
$967$			852868.i			0.912072i	−0.889961	+	0.456036i	$0.849269\pi$
$968$	−289609.	−	160867.i	−0.309073	−	0.171679i
$969$	−253480.			−0.269957
$970$	−790659.	+	256901.i	−0.840322	+	0.273037i
$971$	−372880.	−	270914.i	−0.395486	−	0.287337i	0.372214	−	0.928147i	$-0.378599\pi$
$971$	−372880.	−	270914.i	−0.395486	−	0.287337i	−0.767700	+	0.640810i	$0.778599\pi$
$972$	380468.	−	276426.i	0.402703	−	0.292581i
$973$	41752.7	−	128502.i	0.0441021	−	0.135732i
$974$	−1.09597e6	−	356101.i	−1.15526	−	0.375367i
$975$	−521363.	−	717595.i	−0.548443	−	0.754867i
$976$	−59677.2	+	82138.6i	−0.0626482	+	0.0862279i
$977$	−252268.	−	776402.i	−0.264285	−	0.813387i	−0.991857	−	0.127355i	$-0.959351\pi$
$977$	−252268.	−	776402.i	−0.264285	−	0.813387i	0.727572	−	0.686032i	$-0.240649\pi$
$978$			95372.1i			0.0997112i
$979$	1.31871e6	+	1.16773e6i	1.37589	+	1.21837i
$980$	−770893.			−0.802679
$981$	−475276.	+	154427.i	−0.493865	+	0.160466i
$982$	−80848.7	−	58740.0i	−0.0838397	−	0.0609131i
$983$	1.31752e6	−	957232.i	1.36348	−	0.990627i	0.365267	−	0.930903i	$-0.380978\pi$
$983$	1.31752e6	−	957232.i	1.36348	−	0.990627i	0.998215	−	0.0597245i	$-0.0190222\pi$
$984$	72510.4	−	223164.i	0.0748876	−	0.230480i
$985$	60683.8	+	19717.4i	0.0625461	+	0.0203225i
$986$	−252492.	−	347526.i	−0.259713	−	0.357465i
$987$	47732.3	−	65697.9i	0.0489980	−	0.0674399i
$988$	160695.	+	494569.i	0.164623	+	0.506656i
$989$			1.47090e6i			1.50380i
$990$	887965.	+	386564.i	0.905994	+	0.394413i
$991$	−552727.			−0.562812			−0.281406	−	0.959589i	$-0.590801\pi$
$991$	−552727.			−0.562812			−0.281406	+	0.959589i	$0.590801\pi$
$992$	−153844.	+	49986.9i	−0.156335	+	0.0507964i
$993$	416457.	+	302574.i	0.422350	+	0.306855i
$994$	−258042.	+	187478.i	−0.261166	+	0.189749i
$995$	−349270.	+	1.07494e6i	−0.352789	+	1.08577i
$996$	284788.	+	92533.1i	0.287080	+	0.0932778i
$997$	701494.	+	965524.i	0.705722	+	0.971344i	0.999879	+	0.0155861i	$0.00496143\pi$
$997$	701494.	+	965524.i	0.705722	+	0.971344i	−0.294156	+	0.955757i	$0.595039\pi$
$998$	50966.7	−	70149.7i	0.0511712	−	0.0704311i
$999$	−36372.5	−	111943.i	−0.0364454	−	0.112167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.5.d.a.17.1	yes	16
3.2	odd	2		198.5.j.a.127.3		16
4.3	odd	2		176.5.n.c.17.3		16
11.2	odd	10	inner	22.5.d.a.13.1	✓	16
11.3	even	5		242.5.b.e.241.13		16
11.8	odd	10		242.5.b.e.241.5		16
33.2	even	10		198.5.j.a.145.3		16
44.35	even	10		176.5.n.c.145.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.5.d.a.13.1	✓	16	11.2	odd	10	inner
22.5.d.a.17.1	yes	16	1.1	even	1	trivial
176.5.n.c.17.3		16	4.3	odd	2
176.5.n.c.145.3		16	44.35	even	10
198.5.j.a.127.3		16	3.2	odd	2
198.5.j.a.145.3		16	33.2	even	10
242.5.b.e.241.5		16	11.8	odd	10
242.5.b.e.241.13		16	11.3	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	22.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.68999 + 0.874032i) q^{2} +(-3.20187 - 2.32629i) q^{3} +(6.47214 - 4.70228i) q^{4} +(13.3838 - 41.1910i) q^{5} +(10.6463 + 3.45918i) q^{6} +(-7.80030 - 10.7362i) q^{7} +(-13.3001 + 18.3060i) q^{8} +(-20.1901 - 62.1386i) q^{9} +O(q^{10})\)	\(q+(-2.68999 + 0.874032i) q^{2} +(-3.20187 - 2.32629i) q^{3} +(6.47214 - 4.70228i) q^{4} +(13.3838 - 41.1910i) q^{5} +(10.6463 + 3.45918i) q^{6} +(-7.80030 - 10.7362i) q^{7} +(-13.3001 + 18.3060i) q^{8} +(-20.1901 - 62.1386i) q^{9} +122.501i q^{10} +(90.5882 + 80.2170i) q^{11} -31.6618 q^{12} +(-170.407 + 55.3685i) q^{13} +(30.3665 + 22.0626i) q^{14} +(-138.675 + 100.754i) q^{15} +(19.7771 - 60.8676i) q^{16} +(167.901 + 54.5543i) q^{17} +(108.622 + 149.506i) q^{18} +(213.240 - 293.500i) q^{19} +(-107.070 - 329.528i) q^{20} +52.5217i q^{21} +(-313.794 - 136.606i) q^{22} +564.946 q^{23} +(85.1701 - 27.6734i) q^{24} +(-1011.94 - 735.215i) q^{25} +(409.999 - 297.882i) q^{26} +(-178.970 + 550.813i) q^{27} +(-100.969 - 32.8069i) q^{28} +(505.658 + 695.978i) q^{29} +(284.974 - 392.233i) q^{30} +(276.141 + 849.875i) q^{31} +181.019i q^{32} +(-103.443 - 467.579i) q^{33} -499.334 q^{34} +(-546.632 + 177.611i) q^{35} +(-422.866 - 307.230i) q^{36} +(-164.418 + 119.457i) q^{37} +(-317.087 + 975.892i) q^{38} +(674.423 + 219.133i) q^{39} +(576.036 + 792.845i) q^{40} +(1540.12 - 2119.80i) q^{41} +(-45.9056 - 141.283i) q^{42} +2603.62i q^{43} +(963.502 + 93.2040i) q^{44} -2829.77 q^{45} +(-1519.70 + 493.780i) q^{46} +(-1250.87 - 908.812i) q^{47} +(-204.920 + 148.883i) q^{48} +(687.529 - 2116.00i) q^{49} +(3364.70 + 1093.26i) q^{50} +(-410.687 - 565.262i) q^{51} +(-842.537 + 1159.65i) q^{52} +(-454.551 - 1398.97i) q^{53} -1638.11i q^{54} +(4516.63 - 2657.81i) q^{55} +300.281 q^{56} +(-1365.53 + 443.689i) q^{57} +(-1968.52 - 1430.22i) q^{58} +(3977.33 - 2889.70i) q^{59} +(-423.754 + 1304.18i) q^{60} +(-1508.75 - 490.221i) q^{61} +(-1485.64 - 2044.80i) q^{62} +(-509.644 + 701.464i) q^{63} +(-158.217 - 486.941i) q^{64} +7760.26i q^{65} +(686.941 + 1167.37i) q^{66} -3004.99 q^{67} +(1343.21 - 436.434i) q^{68} +(-1808.88 - 1314.23i) q^{69} +(1315.20 - 955.547i) q^{70} +(-2625.89 + 8081.67i) q^{71} +(1406.04 + 456.849i) q^{72} +(2674.58 + 3681.24i) q^{73} +(337.875 - 465.045i) q^{74} +(1529.76 + 4708.12i) q^{75} -2902.29i q^{76} +(154.610 - 1598.29i) q^{77} -2005.72 q^{78} +(2009.88 - 653.050i) q^{79} +(-2242.51 - 1629.28i) q^{80} +(-2427.13 + 1763.41i) q^{81} +(-2290.15 + 7048.37i) q^{82} +(-8994.67 - 2922.55i) q^{83} +(246.972 + 339.927i) q^{84} +(4494.29 - 6185.86i) q^{85} +(-2275.65 - 7003.72i) q^{86} -3404.74i q^{87} +(-2673.28 + 591.414i) q^{88} +14557.2 q^{89} +(7612.06 - 2473.31i) q^{90} +(1923.67 + 1397.63i) q^{91} +(3656.40 - 2656.53i) q^{92} +(1092.89 - 3363.57i) q^{93} +(4159.17 + 1351.40i) q^{94} +(-9235.60 - 12711.7i) q^{95} +(421.104 - 579.600i) q^{96} +(2097.12 + 6454.28i) q^{97} +6292.94i q^{98} +(3155.59 - 7248.61i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9	\( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9} - 30 q^{11} - 384 q^{12} - 510 q^{13} - 96 q^{14} - 1398 q^{15} - 256 q^{16} + 1770 q^{17} + 1120 q^{18} + 1020 q^{19} - 240 q^{20} + 240 q^{22} - 2424 q^{23} - 640 q^{24} - 858 q^{25} + 480 q^{26} + 2224 q^{27} + 1600 q^{28} + 4890 q^{29} + 3360 q^{30} + 602 q^{31} - 2648 q^{33} - 3904 q^{34} - 8670 q^{35} + 720 q^{36} - 4518 q^{37} - 4800 q^{38} - 1130 q^{39} - 1280 q^{40} + 1290 q^{41} - 3808 q^{42} + 720 q^{44} + 12152 q^{45} + 4480 q^{46} + 642 q^{47} - 128 q^{48} + 9534 q^{49} + 6720 q^{50} - 1500 q^{51} + 4000 q^{52} + 2598 q^{53} + 2582 q^{55} - 3072 q^{56} + 9140 q^{57} - 6496 q^{58} + 6660 q^{59} - 5776 q^{60} - 27410 q^{61} - 19680 q^{62} - 27260 q^{63} + 2048 q^{64} + 2528 q^{66} + 21524 q^{67} + 14160 q^{68} + 11416 q^{69} + 34400 q^{70} - 5562 q^{71} + 10240 q^{72} - 7790 q^{73} + 5760 q^{74} + 3576 q^{75} - 1110 q^{77} - 39424 q^{78} - 2770 q^{79} - 3840 q^{80} - 25464 q^{81} - 17472 q^{82} - 36900 q^{83} - 24480 q^{84} - 24750 q^{85} + 624 q^{86} - 5760 q^{88} + 46596 q^{89} + 55360 q^{90} + 32370 q^{91} + 14112 q^{92} + 20722 q^{93} + 58880 q^{94} + 74250 q^{95} - 3732 q^{97} + 45802 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9 - 30 * q^11 - 384 * q^12 - 510 * q^13 - 96 * q^14 - 1398 * q^15 - 256 * q^16 + 1770 * q^17 + 1120 * q^18 + 1020 * q^19 - 240 * q^20 + 240 * q^22 - 2424 * q^23 - 640 * q^24 - 858 * q^25 + 480 * q^26 + 2224 * q^27 + 1600 * q^28 + 4890 * q^29 + 3360 * q^30 + 602 * q^31 - 2648 * q^33 - 3904 * q^34 - 8670 * q^35 + 720 * q^36 - 4518 * q^37 - 4800 * q^38 - 1130 * q^39 - 1280 * q^40 + 1290 * q^41 - 3808 * q^42 + 720 * q^44 + 12152 * q^45 + 4480 * q^46 + 642 * q^47 - 128 * q^48 + 9534 * q^49 + 6720 * q^50 - 1500 * q^51 + 4000 * q^52 + 2598 * q^53 + 2582 * q^55 - 3072 * q^56 + 9140 * q^57 - 6496 * q^58 + 6660 * q^59 - 5776 * q^60 - 27410 * q^61 - 19680 * q^62 - 27260 * q^63 + 2048 * q^64 + 2528 * q^66 + 21524 * q^67 + 14160 * q^68 + 11416 * q^69 + 34400 * q^70 - 5562 * q^71 + 10240 * q^72 - 7790 * q^73 + 5760 * q^74 + 3576 * q^75 - 1110 * q^77 - 39424 * q^78 - 2770 * q^79 - 3840 * q^80 - 25464 * q^81 - 17472 * q^82 - 36900 * q^83 - 24480 * q^84 - 24750 * q^85 + 624 * q^86 - 5760 * q^88 + 46596 * q^89 + 55360 * q^90 + 32370 * q^91 + 14112 * q^92 + 20722 * q^93 + 58880 * q^94 + 74250 * q^95 - 3732 * q^97 + 45802 * q^99

Introduction

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